It would be a little bizarre if someone with more authority than the Catholic League issued some sort of official statement of deep disappointment regarding the relentless papal corruption — and murder, and fornication, and illegitimate papal offspring, and incestuous undertones — seen in Showtime’s beautiful yet chronically vile new Sunday-night series “The Borgias.”

Suffice to say, the church has enough PR problems without getting exercised about this roughly historically informed depiction of Pope Alexander VI’s unseemly 11-year reign at the turn of the 16th century. So . . . happy Lent, everybody! I hope you didn’t give up television, because this series can be pretty addictive, when it’s not absolutely depressing and dark.

“The Borgias,” created by filmmaker Neil Jordan (“The Crying Game,” “The End of the Affair”), is being billed by Showtime as the original mafia saga. It begins in the auspicious year of 1492, in Rome, where an opportunistic Spanish cardinal, Rodrigo Borgia, schemes to become the next pope.

Borgia is played by the still-fabulous Jeremy Irons, who is loving every evil inch of this role and swishing his garments quite villainously. For those of us who are rusty on our papal history, it takes a moment to dial back five centuries and adjust our eyes to not only the reach and political might the Church once possessed, but also the blatant and contradictory sins that surrounded its leadership.

Like most cardinals of the day, Borgia keeps a palazzo on the side, where the mother of his children (Joanne Whalley as Vanozza) lives in hidden splendor with his son, Bishop Cesare Borgia (a sneeringly handsome Francois Arnaud), military-minded Juan Borgia (David Oakes) and the legendary teen imp Lucrezia Borgia (Holliday Grainger).

A bedridden Pope Innocent VIII breathes his last words to the gathered cardinals with heavy regret: “We have all sullied [the Church] with our greed and lechery. Which of you will wash it clean?”

Cardinal Borgia sets about bribing and bullying the college of cardinals into electing him pope — running flat over their fraying sense of decorum and procedure. The minute the white smoke belches from the chimney, the cardinals suffer an acute case of buyer’s remorse (or seller’s remorse, as the case may be), and some begin scheming to bump him off.

As the triple crown is laid upon Borgia’s head and he becomes Pope Alexander VI, Irons’s face mutates with holy ecstasy and self-delusion — easily the best scene in the first few episodes. He emerges speaking in the royal plural: “I am no longer I,” he marvels. “I am we. We felt so alone out there when the crown touched our head.”

Ta-da! He’s infallible, unstoppable, suffused with money and power, and, from Vanozza’s perspective, he’s a bit too selective with his piety: He tells her they have to cool it now that he’s pope — and also since he’s taken a new lover (Lotte Verbeek as Giulia).

“Must we take vows of poverty, too?” Vanozza wonders.

“Poverty?” the pope replies. “God forbid!”

Cesare prevents a poisoning attempt on his father, strong-arming the would-be assassin (Sean Harris) into working for the family. To shore up his power, the pope appoints a bevy of new cardinals, promoting Cesare to the red-robed rank. A lone renegade cardinal (Colm Feore) flees to neighboring realms, hoping to drum up a war against the Borgia papacy. Thus the series lays groundwork for its subsequent drama, which will be filled with other royals (France’s King Charles, for example) and other historical cameos, such as Machiavelli and even Leonardo da Vinci.

For all its melodrama, “The Borgias” can fall back on Wikipedia for some justification — all of this pretty much happened. But as a piece of popular art itself, the series squanders some of its potential to be something beyond Tony Soprano in a miter. It seems to not quite embrace or make clear its full narrative intent, and it gets old watching Pope Alexander and Cardinal Cesare simmer and scheme.

For bitter or even lapsed Catholics, “The Borgias” can nevertheless be a real scream — and maybe even a guilty pleasure for the still-faithful. If you’re into high-church garb, and your liturgical tastes run to the ultra-traditional (much like our current clotheshorse pope, Benedict XVI), then “The Borgias” could have some “Project Runway” appeal — if nothing else, it really is a lovely effort of period costuming and scenery.

Meanwhile, viewers who ached for the further seasons of HBO’s “Rome” that never came might find some solace in seeing life and death in this Rome, 15 centuries on, still rife with back-stabbing conspiracies and resplendent vanity.

Yet “Rome,” which had characters who vacillated between hero and baddie, also reminds us of what “The Borgias” lacks. In the first four episodes, there isn’t anyone or anything to root for, other than history’s corrective hand.

The Borgias

(two-hour premiere) begins at 9 p.m. Sunday on Showtime.