Amid high hopes for ending a prolonged period of political stalemate in Ireland, Garret FitzGerald of the Fine Gael party formed a government today in coalition with the smaller Labor Party.

The coalition will have a firm parliamentary majority of six, enough to sustain the government through a time of difficult economic decisions and the reestablishment of a dialogue with Britain on the future of Northern Ireland. This is the third new Irish government in 18 months and Prime Minister FitzGerald acknowledged that it faces an "immense task."

FitzGerald, a 56-year-old economist, was prime minister for only seven months when his government fell last winter on the issue of raising consumer taxes. The fall reflected an absence of a consensus on solutions to the country's ills.

This time, in the aftermath of national elections 12 days ago, FitzGerald and the new Labor leader, Richard Spring, a 32-year-old lawyer, have agreed on outlines of an ambitious program committed to reducing 13.5 percent unemployment yet restraining public spending enough to bring the budget into balance and also curb inflation.

Fine Gael, which has 70 seats, is essentially a center-right party on economic issues, while Labor, with 16 seats, is basically center-left. Only by agreeing to tackle the unemployment and fiscal problems together -- even though both parties had to compromise -- could Ireland hope to get the sustained political leadership that all agree is crucial to progress. FitzGerald predicted that his government would survive a full five-year term.

The coalition strategy, hammered out in 10 days of hard bargaining by the two party leaders, calls for establishment of a National Development Corporation intended to provide new jobs through state investment in commercial ventures. The program calls for new taxes on large private houses and a strengthening of taxes on banks and financial institutions.

At the same time, workers will be expected to accept smaller wage increases, some social welfare policies are to be tightened, and the controversial consumer taxes again are to be considered. The target for eliminating the budget deficit is five years, one year more than Fine Gael had pledged.

The outgoing Fianna Fail government of Charles Haughey remains the largest single party in the Dail, as the parliament is called, with 75 members. But FitzGerald and Spring appear to be taking office in a spirit of determination that Haughey seemed unable to inspire and there are persistent reports that he will step down as Fianna Fail leader.

On Northern Ireland, the new government pledged to seek an "honest and positive dialogue" with Britain, a process that broke down over Haughey's refusal to support the Thatcher government during the Falklands war. However, making significant headway on an Anglo-Irish partnership to end the violence in Ulster and devise a meaningful plan for self-government there have been among the most intractable political problems in the world.

FitzGerald is an advocate of making gestures toward Northern Ireland's Protestant community by removing clauses in the Irish Constitution that give special status to Catholics in the republic. The government manifesto opposes violence without "equivocation" while acknowledging the "aspiration to unity" of the Irish people.

As a practical matter, this almost certainly means an early meeting between Prime Margaret Thatcher and FitzGerald to discuss new approaches to the Ulster issue.