And the 34 felony charges, to which Mr. Trump pleaded not guilty, turned out to be more significant and more sweeping than previously suspected. The Manhattan district attorney, Alvin Bragg, described a broad conspiracy, with Mr. Trump at the center, to falsify business records for the purpose of unlawfully influencing the 2016 presidential election. The former president, he said, “orchestrated a scheme with others to influence the 2016 presidential election by identifying and purchasing negative information about him to suppress its publication and benefit the defendant’s electoral prospects.”

It’s been known for a while that the case revolved around hush-money payments that Mr. Trump made to a porn star, Stormy Daniels, to cover up an affair they had. Falsifying business records can sometimes be charged as a misdemeanor in New York State, and to bump up the charges to felonies requires proof that they were falsified to conceal another crime. That crime was widely believed to be a federal campaign finance violation, and some legal experts described that combination as an untested legal theory, because federal violations are outside Mr. Bragg’s jurisdiction.

But it turned out that Mr. Bragg and the grand jury had more than one basis for making the charges felonies. The prosecutor argued on Tuesday that in addition to the federal campaign finance violations, Mr. Trump violated a state election law that makes it a crime to prevent any person from being elected to public office by unlawful means while acting in a conspiracy with others. Mr. Bragg is on much safer ground tying fraudulent business records to a violation of state law, because the defense cannot argue that he lacks jurisdiction on the matter — though Mr. Trump’s lawyers can still argue that state law doesn’t apply to a federal election.

And that wasn’t the only state law that Mr. Bragg said he would cite. The payments to Ms. Daniels were made by Mr. Trump’s lawyer Michael Cohen, who was reimbursed by Mr. Trump in a fraudulent way, the prosecution said. The charging document said this reimbursement was illegally disguised as income in a way that “mischaracterized, for tax purposes, the true nature of the payments made in furtherance of the scheme.” So add state tax violations to the list.

The charges also revealed the breadth of Mr. Bragg’s case, showing he intends to persuade a jury of a conspiracy that extended from Mr. Trump and Mr. Cohen to David Pecker, a former publisher of The National Enquirer, who was allegedly paid $150,000 by Mr. Trump to procure the silence of a second woman with whom Mr. Trump had an affair, the former Playboy model Karen McDougal. It was not certain until Tuesday that the relationship with Ms. McDougal would be part of the case. The felony charges are specifically about Ms. Daniels, but to prove them, Mr. Bragg made it clear that he would describe a much broader pattern of payoffs that included Ms. McDougal.