BOSTON — Harvard University intentionally uses a vague “personal rating” to reject Asian-American applicants in favor of students from other racial backgrounds, according to a trial that started Monday and carries weighty implications for dozens of other U.S. colleges.

Harvard’s legal team denied any discrimination in its opening statement at Boston’s federal courthouse, saying race is just one factor that’s considered and can only help a student’s chances of getting admitted. In its hour-long opening, lawyers for Students for Fair Admissions accused Harvard of intentionally discriminating against Asian-Americans through a “personal rating” score that’s used to measures character traits such as “courage” and “likeability.”

Dozens of supporters and observers packed into the courtroom and two overflow rooms Monday, a day after backers from both sides hosted separate rallies in the Boston area.

The trial began nearly four years after Harvard was sued by Students for Fair Admissions, a nonprofit in Arlington, Virginia, that believes schools should not consider race when selecting students. It comes at a time when the nation’s elite colleges have come under mounting scrutiny over the way race factors into the admissions process.

The suit says Asian-American applicants bring stronger academic records than any other race, yet they are admitted at the lowest rate. The group says that’s because Harvard consistently gives them low scores on the personal rating, which, according to a document revealed by the group Monday, is only loosely defined in Harvard policies.

Lawyers for the group presented a document they say is Harvard’s only guidance on the personal rating. It was simply a numeral rating ranging from one, for “outstanding,” to five, for “questionable personal traits.”

Adam Mortara, a lawyer for Students for Fair Admissions, says the measure’s subjectivity creates an opportunity for racial discrimination.

“You have let the wolf of racial bias in through the front door,” he said.

Students for Fair Admissions is led by Edward Blum, a legal strategist who has fought against the use of race at other colleges, including a Supreme Court case in 2016 that upheld policies at the University of Texas.

Yet Mortara argued Monday the lawsuit is not a broader attack on affirmative action, saying Harvard has simply gone too far in its “zeal” to consider race.

“Diversity and its benefits are not on trial here. Students for Fair Admissions supports diversity on campus,” he said.

But Harvard’s lawyers argued the lawsuit represents an attack on the school and many other universities that consider race as a way to admit a diverse mix of students.

William Lee, a lawyer for the school and a member of its governing board, said race is just one of many factors that can work in favor of an applicant, getting no more weight than a student’s geography or family income.

“Race alone is never the reason a student is granted admission,” Lee said. “And race is never the reason a student is denied.”

He downplayed the influence of any single numerical rating, saying the final decision comes down to a 40-person committee that spends weeks reviewing and discussing applications.

The trial is expected to last three weeks, with two weeks for the plaintiff’s case and one for Harvard. The final decision will be made by U.S. District Court Judge Allison D. Burroughs.

The legal showdown begins amid a revived national debate over the role race should play in college admissions. The U.S. Justice Department is also investigating Harvard over alleged discrimination against Asian-Americans, and Yale was recently announced as the subject of a similar investigation by the Justice and Education departments.

The Harvard case has captured the attention of many in the education world, including leaders of some colleges that say a loss for Harvard could put their own policies in jeopardy.

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