The Empire State is no longer so imperial. With jobs declining and social service costs rising, New York has lined up with the have-not states in a demand for more federal assistance.

That at least is the message written on the wall by a fascinating Democratic race for the Senate seat now held by a venerable but vulnerable Republican, Jacob Javits. The Democratic fight that comes to a head in the primary election next Tuesday includes former New York City mayor John Lindsay, former beauty queen Bess Myerson and Rep. Elizabeth Holtzman.

The political culture of the New York Democracy, until very recently, tended to favor brilliant, sharp-tongued lawyers of a moralistic cast. They would come to Congress, ensconce themselves in the Judiciary committees and take after any straying from the straight and narrow by the White House, the Pentagon, the Central Intelligence Agency or the FBI.

The financial crisis in the Big Apple and the decline of the Buffalo and mill towns along the Erie Canal changed that. In 1976, Pat Moynihan beat out a Republican senator, James Buckley, by promising he could get more federal money for New York.

Myerson picked up that banner when she declared for the Senate last spring.

As a consumer advocate, she had become familiar with the weakened condition of both private and public institutions in the state. As a traveling celebrity, she had come to know, as she put it in an interview the other day, "what people in the other states felt about New York."

So from the start of her campaign, she pushed as her issue the ability to get on with people and win a better deal for New York from the feds. Television spots prepared for Myerson by media consultant David Garth have focused on such issues as mass transit, Medicaid, defense spending and welfare payments. In each, the bottom line is: "She knows how to get things done for New York."

At first that line seemed to play against Holtzman. She is a brilliant lawyer. She served on the House Judiciary Committee. She was particularly active in the Watergate hearings and in pushing for the Equal Rights Amendment. But Holtzman has rallied fast. Her campaign now emphasizes Washington know-how. She points out that she could not have achieved an extension of time for the Equal Rights Amendment or legislation favorable to New Yorkers on "red-lining" and cigarette smuggling without being able to "form coalitions."

Former mayor Linsay also looked vulnerable on the "help New York" issue. He had made his reputation as a congressman zealous in the cause of civil rights and civil liberties on the Judiciary Committee. As mayor, he became known as sponsor of sophisticated programs that cost the city dear.

But he, too, turned the issue around. He has pointed out that, as mayor, he was active with the Conference of Mayors in putting across federal revenue sharing. "New York," he says, "needs a senator whose voice is respected across the country, and whose nerve and resolve have been tested and tempered by experience."

Pollsters working the state say the race is tight. Myerson appears to have a lead, but her campaign has depended on television spots and nobody knows whether her voters will turn out. Holtzman, who has an organization, is confident that with a relatively low turnout, her supporters will carry the day. While Lindsay has run low of funds and is considered a long shot, almost anything could happen. For there is a fourth candidate, District Attorney John Santucci, of Queens, who is an unknown quantity.

If, as seems likely, Myerson or Holtzman wins, Sen. Javits could be in deep trouble. Although popular in the state and one of the best men in the Senate, he is 76 and ailing. The old Rockefeller organization that used to support him is shattered, and he may even have trouble getting voters to the polls in the primary. Holtzman supporters point out that she's half his age. Myerson drives home the point that New York has lowered its sights. "When Javits moved from the Human Resources Committee to Foreign Relations," she says, "he did New York a disservice." c