The shape of Israel's new government-to-be now appears to depend on which of two possible coalitions the Likud Party, which won Tuesday's election with about a third of the votes, will be able to form.

The question is whether Likud will be able to form a broad-based coalition that includes the left-to-center Democratic Movement for Change or whether it will fall back on a narrow and precarious coalition with minor right-wing and religious parties.

The Labor Alignment, which came in second after 29 years in power, has ruled out the possibility of a government of national unity, preferring instead to lick its wounds in the unfamiliar surroundings of the opposition seats.

Much is at stake, for a coalition with the Democratic Movement would nudge the next Israeli government toward the center with a more flexible stand on territorial concessions and a respectability at home and abroad that the other alternative would lack. It would also give the government a comfortable majority, albeit an uncertain one because the two disagree on so many issues.

The narrow coalition with the rightwin and religious parties would be hawkish and nationalistic. Considerable power would flow to the religious parties, enabling them to exact a high price for their cooperation. The working majority of such a coalition would be hair-thin.

The real hagging will begin when the official election results are published in 10 or 12 days. Until then it is a time of unofficial contacts, soul-searching and policy meetings with just about all concerned playing the coalition numbers game. As one Israeli journalist put it, "prognosis must be written as much with a pocket calculator as with a typewriter."

Unofficial election return today gave Likud 43 seats, the Labor Party 32, and right-wing and religious parties 19.

Likud's leader, Menachem Begin, would like to have the Democratic Movement in his coalition but not at the price they are likely to ask. The Democratic Movement would give begin a crack at a comfortable majority and would provide the new government with administrative talent.

The Democratic Movement's leader, archaeologist Yigael Yadin, for example, would be valuable asset in calming the fears of Americans and of many Israelis as well. The Jerusalem Post said in an editorial yesterday. "People have long feared Menachem Begin not because they suspect him of disloyalty to principle, but to the contrary because they viewed him as an unbending doctrinaire."

But Yadin and the Democratic Movement have insisted that any coalition partner accept many of their "sacred" principles, which include a platform against annexation of territory on the occupied West Bank and a demand that elections be held again within two years under a new electoral system.

Likud favors annexation of the West Bank and, although that disagreement might be resolved by both parties promising to go to the people before any final decision is made. Begin is not about to accept new elections in two years. After 29 years in opposition he would like a chance at a full four years in power. So far the Likud has termed the Democratic Movement's principles as "unacceptable."

The Democratic Movement is torn. Some of its leaders say it would be better to stay in opposition and work to pull down the Begin government. Others say it is their duty to join the government and modify Begin's policies - "To save the state of Israel," as one of Yadin's more liberal supporters said.

They also realize that the Democratic Movement is a conglomerate of differing personalities who formed the new protest party only last November. It might soon dissolve in opposition.

Wednesday the Democratic Movement's central committee meets to debate whether or not it should join the Likud-led coalition.

The maddening thing for Yadin's party is that although it came in third with 14 Parliament seats, it failed in its main task. Yadin's stated purpose was to become the balance of power between Likud and Labor - the indispensable coalition partner to anyone trying to form a government. This had not happened and, if necessary, Begin can form a coalition without the Democratic Movement.

Yadin's did not succeed because his party drew votes away from the Labor Party in droves but failed to attract the blue collar, hard hat element that flocked to Likud.

The surprisingly good showing of the National Religious Party, which increased the number of its seats from 10 to 12, makes it possible for Likud to play it tought with the Democratic Movement. Although the National Religious Party used to be a traditional partner of Labor, it now finds itself more comfortable with the right-wing Likud.

To form a government, however, Likud and the National Religious Party need Ariel Sharon, the retired general and founder of Likud, who formed his own party this year and won two Parliament seats. The coalition would also require the participation of two minor religious parties with a half dozen, votes between them - the Aguda Party and the Poalei Aguda.

These parties are deeply Orthodox and emphasize such issues as excluding women from the army draft and a opposition to television. They did not advertise on television during the campaign and traded their allotted TV time to the Labor Party for more radio time.

This narrow coalition would firmly oppose to giving up territory in the biblical land of Israel - the West Bank and Gaza - and wuld probably build more Jewish settlements in the occupied territories.

Such a change in policy would be bitterly opposed by the Arab residents of the West Bank.

The working majority that such a coalition could muster, however, is so thin that Likud is waiting until the army votes are counted to see whether the soldiers will give them a couple of extra seats.