On Monday, U.S. prosecutors will ask 12 people to authorize a punishment that hasn’t been levied on a Manhattan defendant since 1963: death.

Sayfullo Saipov, 35, was convicted last month of fatally mowing down eight people as he raced a truck down a West Side bike path in 2017. Now comes the phase of his trial that will determine his punishment: The U.S. government wants to end Mr. Saipov’s life with a lethal injection.

To succeed, prosecutors must win a unanimous vote from the jurors, who will deliberate in a city that has been both a bastion of liberalism and a stage for repeated acts of terrorism. The clash over Mr. Saipov’s fate will test how a jury in the Southern District of New York — which includes Manhattan, the Bronx, Westchester and five other downstate counties — weighs crime against punishment two decades after 9/11.

The United States has a long history of capital punishment, but the percentage of people who support the death penalty has dwindled. At the state level, New York no longer has a death penalty, a central provision having been ruled unconstitutional in 2004.

But the federal government can still bring capital cases, which is why a jury will gather in a nondescript room in Lower Manhattan to decide whether Mr. Saipov’s act of terror calls for the ultimate punishment.

New York is a global capital of commerce and culture, with 36 percent of its residents born abroad. Around the world, 70 percent of countries have banned the death penalty, including Belgium and Argentina, where six of the bike path victims were from, and Uzbekistan, Mr. Saipov’s native country.

“It’s a really tough question to say whether it’s morally right to exercise the death penalty or not, especially for your everyday person that lives in New York,” said Nick Buenaventura, 29, who stopped his Citi Bike last week to be interviewed near Watts and West Streets, the scene of the attack. “To bear that weight — it’s a heavy decision.”

The Saipov jury faces a stark choice: If the jurors do not unanimously support his execution, he will receive life imprisonment without the chance of release.

The Southern District’s mix of cosmopolitan and rural areas and its diversity of race, ethnicity, financial status and political viewpoints would seemingly ensure defendants can have their cases heard by a cross-section of the community. In a death penalty case, however, the jury’s composition is tilted in the government’s favor, because people unalterably opposed to capital punishment are not allowed to sit on the jury.

Michael B. Mukasey, the attorney general under President George W. Bush from 2007 to 2009 and before that a longtime Southern District judge, thinks a death penalty could be imposed. “New York is famous as a place where people can be realistic in a hard-nosed way,” he said, adding that with a spike in crime in the city, “I would by no means bet the farm on it being impossible for a jury to return a death penalty verdict in this case.”

Mr. Saipov’s lawyers’ advantage is that they must persuade only a single juror to hold out. Rachel E. Barkow, a law professor and sentencing expert at New York University, said that could make it harder for the government to obtain a death penalty verdict.

“That’s difficult in any circumstance,” said Ms. Barkow. “It’s particularly difficult with a Southern District jury in Manhattan.”

Death penalty trials are rare in New York State and even rarer in Manhattan.

The last federal executions in New York State, all stemming from Southern District trials, occurred almost seven decades ago: Gerhard A. Puff, a bank robber who killed an F.B.I. agent, was executed in 1954.

The previous year, Julius and Ethel Rosenberg died in the electric chair after a Southern District jury found them guilty of conspiring to steal atomic secrets on behalf of the Soviet Union. They each denied throughout their trial that they had been spies, and after they were electrocuted, acrimonious debate over their convictions continued through the decades.

The last state execution was in 1963, when Eddie Lee Mays, 34, was put to death for killing a woman in a bar in Harlem.

Federal prosecutors have continued to pursue the death penalty in Southern District cases in Manhattan, but without success.

In the months before 9/11, a Southern District jury twice voted 9 to 3 on the question of whether to execute two operatives of Al Qaeda who conspired with Osama bin Laden in the 1998 bombings of two United States Embassies in East Africa that killed more than 220 people, including 12 Americans. The lack of unanimity resulted in life sentences.

Southern District juries also rejected death in two later trials — a 2004 case of two Bronx heroin dealers convicted of the murder of a police informant and a 2005 case involving a father and son convicted of three killings in a dispute over a cocaine deal.

Stephen B. Bright, a lawyer who has represented death penalty defendants in Alabama, Mississippi and Georgia and teaches at Yale Law School, said that the likelihood that a jury would impose the penalty depended to a great extent on the population from which the jury was chosen.

“You try them in, say, the Southern District of Alabama, in Mobile, Ala., you’re going to have a very different outcome,” he said.

Brad Hoylman-Sigal, a Manhattan state senator and chairman of the body’s Judiciary Committee, said that although the bike-path murders were horrific, he hoped at least one juror would stand against the death penalty.

“It has had such a problematic history, and surely New Yorkers understand that,” Mr. Hoylman-Sigal said. “I’m hopeful that the jury thinks better of it and understands that the fitting punishment for this crime is life imprisonment.”

Nationally, when people were asked whether punishment for murder should be the death penalty or life imprisonment without parole, 60 percent chose the latter, according to a 2019 Gallup survey.

Recent surveys of New Yorkers’ attitudes on capital punishment are rare. A Quinnipiac University poll in 2003 showed that when offered the choice between death and life without parole, only 38 percent favored execution.

In New York State, the death penalty hasn’t been a pivotal election issue since 1994, when George E. Pataki, a Republican candidate for governor, vowed to bring it back. He won statewide, but New York City residents voted more than two to one for his opponent, Gov. Mario M. Cuomo, who had vetoed a dozen death penalty bills.

In March 1995, Gov. Pataki signed a measure reviving capital punishment, but a court struck it down in 2004, and no executions took place while it was back on the books.

Mr. Saipov’s case is notable because he is the first defendant to face a federal death penalty trial during the administration of President Biden, who had campaigned against capital punishment.

During testimony in January, evidence showed that Mr. Saipov drove a rented pickup truck across the George Washington Bridge into Manhattan on Halloween Day 2017, then turned onto the bike path and sped south, smashing into cyclists before crashing into a school bus.

Ann-Laure Decadt, 31, a Belgian woman visiting with her two sisters and mother, was one victim. They had rented their bikes from a store called Blazing Saddles.

Dyshea Smiley, 35, a tour guide for Blazing Saddles since 2015, recalls the day of the attack clearly. “I just remember the silence after,” she said, adding, “Can you imagine a family of yours going on vacation and never coming back?”

Ms. Smiley said she had strong feelings about Mr. Saipov’s punishment.

“I would give him the death penalty,” Ms. Smiley said. “I don’t care about his life — he didn’t care about human life.”

Gwyneth Leech, 64, an artist who has lived in New York since 1999, still uses the bike path, navigating bollards installed after the attack to keep motor vehicles away. She said a memorial plaque regularly reminds her of the lives lost, but that reverence does not require retribution.

“I’m opposed to the death penalty, so that’s it,” she said.

Mr. Saipov’s lead lawyer, David E. Patton, the city’s federal public defender, acknowledged during the trial that his client had acted intentionally and had caused “unimaginable pain and suffering.” But he disputed the government’s contention that Mr. Saipov was fixated on joining the Islamic State terrorist group. He said his client had acted alone after spending hours caught up in propaganda and martyrdom videos.

Mr. Patton has said in court that the defense plans to bring members of Mr. Saipov’s family to the United States to testify on his behalf, presumably to offer the jury a fuller portrait of Mr. Saipov, his childhood, his upbringing in Uzbekistan, his solitary hours on the road as a long-haul truck driver.

Austin Sarat, a professor of law and political science at Amherst College, who has written critically about capital punishment, said that Mr. Saipov’s defense lawyers must change his image in jurors’ minds.

“The burden that the defense faces is to turn this man from a terrorist into a human being,” said Mr. Sarat.

Prosecutors, in court filings, have cited various factors that they say favor execution, including that Mr. Saipov’s attack was premeditated and carefully planned and that it was carried out in support of a terrorist organization.

The arguments over whether Mr. Saipov should live or die could last into March. Then, the 12 New Yorkers will retreat into the jury room to decide.

“I’m glad that I’m not on the jury, because I truly don’t know,” said Mr. Buenaventura, the man interviewed on the bike path. “It’s a real morality decision.”

Brittany Kriegstein contributed reporting. Susan C. Beachy contributed research.