A diet of bread, water and peanut butter. A laptop with no internet connection. And intermittent access to millions of pages of digital evidence.

Sam Bankman-Fried, the 31-year-old cryptocurrency mogul, has spent nearly a month at the Metropolitan Detention Center in Brooklyn since a federal judge revoked his bail in August. As Mr. Bankman-Fried prepares for a fraud trial next month over the collapse of his crypto exchange, FTX, his lawyers have offered a picture of the conditions he has faced at the jail — a far cry from the Bahamas penthouse he once shared with other billionaire executives.

In a series of court filings, Mr. Bankman-Fried’s lawyers have raised issues such as the disruption to his vegan diet in jail, as well as his dwindling supplies of prescribed medication like Adderall, which treats A.D.H.D. They have also said he has not been getting enough access to the internet to prepare for his trial and should be released.

On Tuesday, those lawyers and the prosecutors bringing the case continued to argue in letters to the judge over whether enough accommodations have been made so that Mr. Bankman-Fried has access to a laptop and consistent internet service to review materials for trial. They did not reach a resolution, leaving it for the judge to decide.

A representative for Mr. Bankman-Fried declined to comment. A spokesman for the Federal Bureau of Prisons, which oversees the Brooklyn facility, declined to comment on Mr. Bankman-Fried’s conditions but said that the M.D.C. offered “access to health care, telephones, a law library for legal research, hot meals,” and that the people held there lived in “certified environmental conditions.”

FTX collapsed in November, a symbol of crypto hubris gone awry. Since then, Mr. Bankman-Fried had spent months in relative comfort. After his arrest on fraud charges in December, he pleaded not guilty and was granted bail, allowing him to live in his parents’ home in Palo Alto, Calif. He was able to play video games and watch sports, while meeting with reporters and working with lawyers to construct a defense.

Last month, the judge overseeing his case, Lewis A. Kaplan, revoked Mr. Bankman-Fried’s bail after ruling that the FTX founder had twice tried to interfere with witnesses in the case. Mr. Bankman-Fried was taken from the courthouse to the M.D.C., a jail that has struggled with staffing shortages, freezing conditions and other problems.

Mr. Bankman-Fried’s lawyers have filed an appeal seeking to have his bail reinstated. At a hearing last month, Mark Cohen, one his lawyers, said the jail was not accommodating Mr. Bankman-Fried’s vegan diet, forcing him to subsist on bread, water and peanut butter.

“Notwithstanding multiple requests for a vegan diet, he continues to be served a flesh diet,” Mr. Cohen said in court.

Mr. Cohen also asked Judge Kaplan in a filing to give Mr. Bankman-Fried access to two medications that have been prescribed to him — Adderall and Emsam, a transdermal patch that treats depression. Mr. Bankman-Fried had taken only a few days’ worth of the medications with him to the jail, Mr. Cohen said.

Recently, most of the back and forth in court has focused on Mr. Bankman-Fried’s access to the millions of pages of digital evidence in the case.

In filings last month, his lawyers argued that the M.D.C.’s conditions had made it virtually impossible for him to prepare for the trial. Mr. Bankman-Fried has access to an offline laptop that he can use during visiting hours, with his lawyers present, the filings said. But he cannot reach a key database of materials that is available only via the internet.

Twice a week, Mr. Bankman-Fried is allowed to leave the jail and meet with his lawyers at the federal courthouse in Manhattan, according to the filings. But an internet-enabled laptop he was given for those meetings has limited battery life, and Mr. Bankman-Fried has not been permitted an extension cord to charge it, the lawyers said. The internet connection has also been shaky.

“Time and again the government’s promises around providing him bona fide access to discovery have proven empty,” Mr. Bankman-Fried’s lawyers wrote in a filing.

In their own filing, the prosecutors have said the Bureau of Prisons’ “nationwide security policies prohibit the use of any internet-enabled electronic device within the prison.”

In a Tuesday letter to the judge, prosecutors said that to get around that prohibition, they had allowed Mr. Bankman-Fried to use a laptop that could connect to the internet two days a week at a special inmate holding facility in the federal court in Manhattan. They said that in general, internet service had been “sufficient for most internet review activities.”

But his lawyers disputed that characterization in their own letter and said they were “skeptical that the cellblock procedures will work as promised.”

The overall conditions at the M.D.C., which houses more than 1,500 male and female detainees in traditional cells and dormitory-style rooms, have long been a source of concern. When he revoked Mr. Bankman-Fried’s bail, Judge Kaplan acknowledged that the M.D.C. was “not on anyone’s list of five-star facilities.”

In February 2019, M.D.C. detainees endured subfreezing temperatures when a nearly weeklong power outage left the jail with limited heat and electricity. Last year, the National Association of Criminal Defense Lawyers issued a statement that said M.D.C.’s conditions were “inhumane” and noted that it had “the highest number of Covid-19 positive detainees in the nation” during the pandemic.

Ghislaine Maxwell, a former associate of the disgraced financier Jeffrey Epstein, frequently complained about the jail’s harsh living conditions when she was detained there before her trial on sex trafficking charges. She described it as “a living hell.”

The Bureau of Prisons spokesman said the M.D.C. provided “essential medical, dental and mental health services” and followed protocols designed to ensure appropriate temperatures for winter and summer.

Before they started working for Mr. Bankman-Fried, Mr. Cohen and his partner, Christian Everdell, helped represent Ms. Maxwell. While she was in the M.D.C., they argued that Ms. Maxwell needed access to a laptop to review discovery materials on weekends and holidays.

A judge granted that request over an objection from the Bureau of Prisons.