Urban progressives took over the New York state Senate in November, but the body’s biggest swing group will be suburban Democrats. These Democrats will need to prove themselves to their voters, many of them homeowners in places like Long Island and West­­chester.

The most valuable deliverable for the nascent suburban caucus will be a permanent extension of Gov. Cuomo’s property-tax cap.

Enacted in 2011, Cuomo’s first year in office, the law limits the annual growth in total property-tax levies to 2 percent or the rate of inflation, whichever is less, in all fiscally independent school districts and all counties and municipalities outside the Big Apple. It can be overridden by 60 percent of the members of local governing bodies or by an equally large supermajority of taxpayers voting directly on school budgets.

Cuomo’s cap has curbed taxes by billions of dollars, compared to previous trends and especially in profligate school districts.

There is just one problem: The tax cap is temporary. At the insistence of then-Assembly Speaker Sheldon Silver, who had no use for the cap to begin with, the cap was awkwardly inserted as a provision of the state law regulating city apartment rents. Although it dates back to the 1970s, the rent law itself is temporary, sunsetting every few years.

When the rent law was last extended, in 2015, the cap was extended, too. The rent regulations are next due to expire in mid-2019, with the tax cap’s expiration set for a year later if those laws aren’t extended.

When the cap was last renewed, a tenuous 32-31 majority of Republicans controlled the Senate. The GOP majority strongly supported the tax cap while also backing landlords who resist tighter rent regulations.

In last month’s election, however, the Senate flipped to a 40-member Democratic majority, while Democrats retained their supermajority in the Assembly.

In January, members from New York City will dominate the majorities in both houses. They will be less interested in controlling property taxes than in strengthening and expanding rent regulations.

But this doesn’t mean the more solidly Democratic Legislature can ignore or try to weaken the tax cap. To the contrary: 11 downstate suburban senators can effectively wield the balance of power on this issue. The pivotal core of the Senate’s new, downstate suburban caucus consists of a half-dozen Long Island members.

Todd Kaminsky of Long Beach will be their de facto leader. Kaminsky was first elected in 2016 to the Senate seat held for 31 years by Dean Skelos, the former Republican majority leader now headed to prison after his conviction on federal corruption charges.

Kaminsky and the rest of the Senate Dems’ winning Long Island slate appeared with Cuomo at an October campaign rally, where they pledged to back the governor’s policy priorities, including the property-tax cap and Cuomo’s self-imposed 2 percent limit on state spending, along with a general promise to “hold the line on taxes.”

Pressing for yet another temporary extension of the measure — with absolutely no added loopholes that would allow school districts to skirt the cap — is the least the suburban Democrats can do to demonstrate their commitment to property owners.

To really make a mark, and to defy GOP pre-election warnings that they’ll behave like tax-and-spend liberals, the suburban Democrats should fight next year to make the tax cap a permanent, stand-alone law. This was something Senate Republicans advocated but could never accomplish.

A permanent tax cap should also find support among the five Democratic state senators from the heavily taxed lower Hudson Valley — including new Senate Majority Leader Andrea Stewart-Cousins of Yonkers, whose district includes some of the most affluent communities in central Westchester.

Kaminsky, for one, seems to get the general idea, telling Newsday after the election that the new delegation isn’t “going to let their voters down.” He added: “I think the mistakes of the past are readily apparent to everyone.”

This was a reference to the Democrats’ brief previous term of Senate control in 2009, when they passed a regional payroll tax to prop up the finances of the Metropolitan Transportation Authority. That tax package was widely blamed for the 2010 defeat of two Long Island senators, which allowed Republicans to regain control of the upper house.

“We want to stay in the majority . . . to be a growing and effective majority,” Kaminsky said.

A permanent tax cap would help them earn it.