Former President Donald Trump’s company, the Trump Organization, faces a tax fraud lawsuit this week — related to what prosecutors say was a 15-year scheme by top company officials to hide profits and avoid paying taxes.

Prosecutors say that for years the former president’s illegal wealth empire helped top executives avoid income taxes by giving them fringe benefits such as rent-free apartments and luxury cars.

The trial begins today in New York with opening statements and testimony.

Among the key witnesses for prosecutors are former Trump company chief financial officer Allen Weisselberg, who pleaded guilty and also agreed to testify in exchange for a five-month prison sentence.

If convicted, the Trump Organization could be fined more than $1 million. Although the amount of the fine is affordable for the company, the biggest damage will be the inability in the future to secure credit and enter into new contracts. Some partners and government institutions may seek to sever ties with the company.

Neither Mr. Trump nor any of his children who worked as executives of the Trump Organization have been charged. Former President Trump is not expected to testify or attend the trial.

However, he will be indirectly present as his name is synonymous with the Trump Organization, through which the former president manages his many ventures, including his investments in golf courses, luxury villas and other real estate and his many marketing deals.

Mr. Trump has signed some of the checks on which the case rests. His signature appears on many company documents. Witnesses can testify about the conversations they had with him. They are even expected to have access to Mr. Trump’s personal ledgers.

The Trump Organization has said it has committed no wrongdoing. The company’s lawyers argue that Mr. Weisselberg and the other executives acted individually and that even their actions harmed the company financially.

Mr. Weisselberg, who has pleaded guilty to receiving $1.7 million in compensation without registering it, said he and other top Trump Organization executives, including Vice President Jeffrey McConney, were individually responsible.

But he denies that the company was harmed, saying that their benefits actually saved the company money, since it was not obligated to give them additional financial compensation.

Prosecutors have said they will call 15 witnesses, including Mr. Weisselberg and Mr. McConney, who were granted limited immunity last year to testify before a grand jury.

Judge Juan Manuel Merchan expects the trial to last at least four weeks, although a defense lawyer estimated last week that only the prosecution’s case could continue for two months.