CHICAGO — J. Dennis Hastert, once among the nation’s most powerful politicians, was sentenced on Wednesday to 15 months in prison for illegally structuring bank transactions in an effort to cover up his sexual abuse of young members of a wrestling team he coached decades ago.

In a hearing that was by turns harrowing and revelatory, Mr. Hastert publicly admitted for the first time to abusing his athletes, was confronted in emotional addresses by one of the former wrestlers and the sister of another, and faced a long, scathing rebuke from the judge.

Mr. Hastert, 74, who made an unlikely rise from beloved small-town wrestling coach in Illinois to speaker of the House in Washington, sat slouched in a wheelchair in a federal courtroom here as a judge announced that he was rejecting pleas for probation from Mr. Hastert’s lawyers, as well as prosecutors’ endorsement of a shorter prison stay.

While the sentencing hearing was, technically, about a violation of banking rules and regulations, the proceedings focused squarely on the underlying reason for Mr. Hastert’s puzzling bank withdrawals — his abuse of young wrestlers who had viewed him as a role model.