An intriguing new series with a far-fetched premise, “New Amsterdam” (8 p.m., Fox) stars Nikolaj Coster-Waldau as John Amsterdam, a New York City detective with a special secret. He’s been hanging around the Naked City since 1642.

We learn that Amsterdam was actually a Dutch soldier who, in return for saving a Native American maiden’s life, received a special gift of near immortality. He’d cheat death and live on until he found his soulmate.

OK, I told you it was far-fetched. But it’s not so silly as to scuttle a smart and strangely romantic detective show.

Amsterdam continually surprises his fellow cops, particularly his partner, Eva (Zuleikha Robinson), with his arcane knowledge. How does he know that a particular building used to house a speakeasy or that a hotel room contained a special mural and a hidden doorway? Because he was there. Back in the day. Way back. You just can’t find cops anymore with his “institutional memory.”

Amsterdam’s special gift (or burden) brings an added dimension to the brooding-detective genre. It far surpasses “Moonlight,” the vampire-private-eye show over on CBS.

And Amsterdam’s search for a love that will bring him happiness (and death) puts this show in the dark mythic territory of “Pushing Daisies.”

Amsterdam shares his secret identity with Omar (Stephen Henderson), a jazz-club owner with some secrets of his own.

Omar has seen Amsterdam “die” and return many times over. We have no idea what Omar’s real age is, either.

We do know that they both spent time with jazz legends John Coltrane and Thelonious Monk in another New York, a long, long time ago.

The detective is not shy about talking about his many pasts. He tells Eva that he was left partially deaf during the storming of Normandy Beach. He declares before his AA meeting that he’s been sober for thousands of weeks. But everyone dismisses his statements as wisecracks and hyperbole. In many ways, he’s been hiding in plain sight.

He also spends his downtime in his wood shop. He re-creates furniture that he was famous for making centuries before. You could say he was in the antiques business.

¢ With its depiction of New York as a place of history, myth, legend, tradition, jazz, writers and vibrant life and violent change, “New Amsterdam” may be the most romantic TV look at the Big Apple in some time. The same cannot be said of “The Real Housewives of New York City” (10 p.m., Bravo), another needless showcase for the hateful, vulgar, rich and spoiled who treat Manhattan (and the entire world, for that matter) as their own private shopping mall.

Tonight’s other highlights

¢ The eight remaining guys perform on “American Idol” (7 p.m., Fox).

¢ Look for continuing coverage and analysis of primary results from Ohio and Texas (7 p.m., CNN, Fox News, MSNBC).

¢ Hawkins receives a disturbing phone call on “Jericho” (9 p.m., CBS).

¢ People confront challenges on “Primetime: What Would You Do?” (9 p.m., ABC).

¢ Andrew Zimmern hosts the second-season premiere of “Bizarre Foods” (9 p.m., Travel).