Louisville had implemented those punishments in 2016, after the scandal came to light but before the N.C.A.A. could rule on it. They included sitting out that season’s Atlantic Coast Conference and N.C.A.A. tournaments despite a highly regarded squad.

This year, under an interim head coach, the Cardinals are 18-9 over all and 8-6 in the A.C.C. They are considered a better-than-average contender to qualify for the N.C.A.A. tournament even as they face new accusations of improper recruiting.

Several months ago, Louisville was one of six programs — and perhaps the most prominently figured — implicated in a broad bribery and corruption scheme outlined by federal investigators. In one complaint, investigators described a partnership involving Louisville basketball coaches and several other parties, including a former executive at Adidas, the apparel company that sponsors Louisville’s teams, in which they planned to funnel $100,000 to the family of a recruit in exchange for his commitment to the Cardinals.

That scandal led to the ouster of Pitino and Louisville’s athletic director, Tom Jurich, by the university’s board. Pitino has sued Louisville for breach of contract, and Louisville has countersued. Those cases are pending.

An attorney representing Pitino did not immediately reply to a request for comment Tuesday.

It is unknown what the broader implications of the latest recruiting scandal will be on Louisville or any other program, or on college basketball itself. The N.C.A.A. has convened a commission to examine reforms to the sport in light of the scandal, which also implicated several other top programs.

Tuesday’s ruling will sting at Louisville, which must surrender its 2013 national title less than six months after a conference rival, North Carolina, was able to avoid sanctions when the N.C.A.A. ruled that it had broken no rules in a major academic scandal involving dubious classes disproportionally taken by major-sport athletes. An adverse finding there could have stripped the Tar Heels of at least one national championship, and possibly more.

The title Louisville was ordered to surrender, won with an 82-76 victory over Michigan, will remain vacant, even though Postel, in his statement, urged Louisville fans to retain their claim to it.

“The N.C.A.A.’s ruling,” he wrote, “cannot change the accomplishments or the excitement generated by our Cardinals basketball team.”