Quebec's new Premier, Rene Levesque, arrives in New York City on Monday for two days of crucial meetings with U.S. bankers and financial executives and a major address Tuesday night before the Economic Club of New York, whose membership includes many of this country's most important business leaders.

Levesque faces the formidable task of convincing the financial community here that there is nothing to fear in the recent election triumph of his Separatist Parti Quebecois, and that U.S. capital should continue to flow liberally into his province's economy which is heavily reliant on American financing.

At the same time, he cannot appear to back off from the issues of political and economic independence for Quebec that brough him to power without risking disaffection among his supporters at home.

The conflict has become exacerbated in recent days with a further deterioration in Quebec's 1977 economic outlook, which in turn pressures Levesque to come up with the funds to stimulate the province's economy because economic discontent even more than separatism is believed to have caused the surprisingly heavy vote for the parti Quebecois.

The Conference Board of Canada, a business research organization, last week said "prospects for growth in real domestic production in Quebec in 1977 appear considerably less optimistic now than in the fall" when the last report was issued, with growth in real output expected to be about 2.75 per cent compared with just over 3 per cent for the Canadian economy as a whole, and a long-term growth trend of about 5 per cent.

"The anticipated sluggish performance of the economy of Quebec reflects downward revisions in the growth prospects of most industries, including forestry, mining, manufacturing, construction and services," the report said, adding that the slow growth should increase the province's average unemployment rate to "over 10 per cent" in 1977 from 8.7 per cent in 1976.

Levesque's surprise victory last November sent shock waves not only through Canada, but also through. Amerian business and financial circles which over the years have made substantial direct investments in Quebec and which also have been important suppliers of capital for both the government of the province and its massive state-owned utility, Hydro-Quebec. Last year alone, nearly $1.5 billion was borrowed in U.S. money markets.

The concern stemmed first from Levesque's deep commitment to a political separation of French-speaking Quebec from the rest of Canada, with unknown consequences for relations with the U.S. should he succeed.

But because polls have indicated that only about 18 per cent of Quebec residents would vote for separation, perhaps more disturbing to many investors is his economic philosophy which is perceived as socialistic - albeit on the Scandinavian model of Democratic Socialism - and during the election campaign vague proposals also were made to expropriate basic industries in the province.

In an article in Foreign Affairs maganne last July titled "For and Independent Quebec," Levesque complained about "the stifling remote control of nearly all major decisions either in Ottawa or in alien corporate offices."

In that article, Levesque called for a policy of economic "repatriation," which he said involved "full legislative control" over Quebec's financial institutions and a break of "the strangle-hold" of the "British-inspired banking system" were a few major banks have "always kept the people's money and financial initiative."

For nonresident corporations, Levesque proposed an "investment code" which would spell out what areas would be reserved for home ownership, including "basic steel and forest resources," those sectors where mixed control would be allowed and, "finally, the multitude of fields (tied to markets, and to technoligical and or capital necessities) where foreign interests would be allowed to stay or to enter provided they do not tend to own us along with the business."

For the last several years Canada as a whole has been hostile to American investments.Analyzing the Canadian and Quebec situation soon after the election, Eric Rinner, an economist with Loeb, Rhoades & Co., a New York investment banking firm, woundered whether the economic environment in Canada, and especially in Quebec, for American direct investment and for the operation of American multinationals will further deteriorate."

Triggered by the election, the Canada dollar dropped about 5 per cent in relation to the U.S. dollar in foreign exchange markets (it has partially recovered since then), and the price of Quebec Province and Hydro-Quebec bonds dropped significantly in relation to securities issued by other Canadian provinces, indicating that an interest rate penalty should be expected on future borrowings.

Given this suspicious and uncertain psycholigy within the investment community here toward Quebec, Levesque's job show first that he is no wild-eyed radical, then to specifically lay out what his plans are with respect to the province's economy, his attitude toward external investment and his plans on when to hold a referendum on whether to separate from the rest of Canada.

"There are an awful lot of things that U.S. investors would like to hear spelled out," says Richard J. Schmeelk, the U.S. cochairman of the prestigious Canadian-American Committee, which studies economic relations between the two neighboring countries, and who is a partner in the investment banking firm of Salomon Brothers, which underwrites many Canadian securities offerings in U.S. markets. Schmeelk calls the Economic Club speech "very important" in this respect, and notes that Levesque, a former broadcaster and commentator, is noted for his oratorical eloquence and persuasiveness.

A press spokesman for Levesque agreed that the "Economic Club is an important group and this is an important visit." The spokesman said Levesque "will try to give them the picture of where we are going immediately and mid-term, and what his intentions are. The questions arising from the financial world are legitimate and he wants the financial community of New York to have as exact an image of our government as possible.

The two days in New York will otherwise be spent in private meetings with various lenders, including commercial banks, investment bankers and insurance company officials, the spokesman added.

Last year, the Province of Quebec borrowed $1.335 billion, with $710 million raised within Canada, $100 million in the United States, and $325 million in European money markets.

Hydro-Quebec, the state-owned utility which Levesque formed in the early 1960s when he served as Quebec's minister of natural resources under the liberal party government, is engaged in a $18 billion by hydroelectric project in Quebec's James Bay, perhaps the largest capital project in the world at present. Last year, the utility borrowed $1.77 billion, with $1.3 billion coming from the U.S., including a $1 billion private placement (a record for any foreign entity), $189 million within Canada and $281 million Europe.

An investment banker who is familar with Quebec's past borrowing and who asked that his name not be used indicated that investors here would continue to lend money more readily to Hydro-Quebec, because they feel they have a lien on the project, then to the province itself.

But he noted that in 1977 it is more likely Quebec Province, which is running about a $1.3 billion deficit for the fiscal year ending March 31, and which probably will run an even larger deficit in the following year, will be in need of the larger sums and have to come to the New York money markets in size.

"But if the province came down here now, the size it could do would be less than in previous years and it would also have to pay a substantial penalty," he said.

Quebec bonds are now already trading at about 1 per cent more in than the bonds of neighboring Ontario Province - an increase in the spread of 0.5 per cent since the election - and about 1.25 per cent above the highest-rated U.S. corporate bonds.

The investment community largely believes that any proposed referendum for Quebec to secede from Canada would almost certainly be defeated by the voters of the province, so there is not much real concern on that score, the financial official said.

But as to what potential investors would like to hear from Levesque to allay their real fears, the investment banker said, "They realize he has to move ahead to try to stimulate the economy, but they don't want him to do it with stimulation through nationalization."

He noted that Rhodrique Tremblay, Quebec's new minister of industry and trade, recently soft-pedaled any talk of socializing industry and emphaized instead the desire of the current government to get the province's economy moving with outside financial assistance.

And he predicted that Levesque now would similarly downplay the possibility of the Quebec government taking over any industry, except perhaps asbestos mining. In the asbestos companies in Quebec are not very good corporate citizens anyway" because of unsafe labor conditions, he said, indicating that resistance to a takeover therefore would be less.

Interestinyly, when Levesque took over a number of privately owned untilities in the early 1960s to form the basis of Hydro-Quebec, "shareholders were amply compensated and there were no complaints," the banker pointed out. "It was done very smoothly and fairly. So he has a history of being very fair with shareholders."

There is also a pattern of no interference by the Quebec government in theoperations of Hydro-Quebec, though it is state-owned, which appeals to investors and in the utility, the Wall Street official added.

The ready availability of vast amounts of cheap hydroelectric power at a time of soaring prices for competitive energy sources is one of Quebec's most important long-term economic assets, along with abundant forest reserves and other natural resources, its strategic geographic position astride the St. Lawrence Seaway, and a large pool of manpower.

However, Quebec, which is Canada largest province in size and second to to neighboring Ontario in population, has been less economically prosperous than the company as a whole, and then its neighbor Ontario in particular.

With 6.2 million residents (80 per cent of whom are French Canadians), or 27 per cent of Canada's population, Quebec accounts for only about 21 per cent of the country's gross domestic products. And between 1971 and 1975, Quebec's compound annual growth rate in fixed dollars was 4.6 per cent compared with 5.3 per cent for Canada as a whole.

The province also suffers unfavorably in comparisons involving unemployment, salary levels, retail trade and other measures of economic well-being.

While Quebec in the past has been able to attract more than its share of private investment capital, primarily because of the availability of a large and cheap labor force, that situation no longer obtains and a turbulent series of strikes has further soured outside investors to the point where it is believed more capital is now flowing out of Quebec than into the province.