FAIRFIELD, Conn. — Last night, the first official basketball game at Fairfield University’s brand-new, 85,000-square-foot Leo D. Mahoney Arena took place. The building, which cost $51 million, takes pride of place in the center of campus.

Across Loyola Drive, in the suite of admission and financial aid offices in the Aloysius P. Kelley Center, the school has hit a different kind of milestone: The class of first-year students that entered in 2020 had the lowest percentage of Pell Grant recipients of any college in the United States — 7.5 percent — according to the most recent federal data.

The federal government makes Pell Grants available to students from families with the lowest incomes in the country. So the figure has become a proxy for a higher education institution’s commitment to pulling students up from the lowest rungs of the social-class ladder.

Is the Pell Grant the best metric to judge this commitment? Fairfield, a Jesuit institution whose mission includes fostering “ethical and religious values and a sense of social responsibility,” believes the measurement is “not particularly useful” or “modern.” The school refused to let administrators have an on-the-record conversation with me about it, but I did communicate by email with one vice president.

“Built upon the bedrock of a sustainable academic and economic model, we continue to work to make Fairfield more accessible to as many students as possible,” Corry Unis, who has been the school’s vice president for strategic enrollment management since 2018, said in an email.

The words “sustainable” and “economic” do offer some clues as to how the school ended up with such a low Pell figure — and to how difficult and expensive it can be to reverse this at a university with 4,757 undergraduates.

The first class of students was admitted to Fairfield in 1947. In university years, that’s fairly young. It is too young, in this instance at least, to have enough graduates who have made and donated sufficient money to the school’s endowment to meet the full financial need of every student the school accepts.

Federal data tell some of that story. In the 2020-21 school year, first-year, full-time Fairfield undergraduates whose families had incomes of $30,000 or less paid an average “net price” of $31,018. Up the road at Trinity College in Hartford, a school with a much higher endowment per student, that figure is $8,252. At Providence College in Rhode Island, it’s $19,531.

How can families pay $31,038 to Fairfield when they earn no more than $30,000? The government defines “net price” in this instance as what families are responsible for after Pell Grants are subtracted from a school’s list price (about $70,000 at Fairfield this year, including room and board). Pell Grants amount to no more than $6,895 per student for the 2022-23 school year and go most often to families with incomes under $60,000. Any state or local government scholarships are also subtracted from the list price, as are whatever additional grants an individual school offers. A family or student covers the remaining net price with savings, income and loans.

James Murphy, a senior policy analyst at the advocacy group Education Reform Now, generates the Pell rankings each year and publishes the results on the organization’s website. He dove a little deeper into Fairfield’s first-year student numbers and found that its percentage of Pell recipients had dropped 44 percent over four years, to 7.5 percent in 2020-21 from 13.3 percent in 2016-17.

“How does that happen?” he asked. “Choices are being made. You have to assume it’s someone pretty high up the ladder.”

At the very beginning of a speech in September, Fairfield’s president, Mark R. Nemec, practically beat his chest with pride. “We are now the seventh most selective Catholic university,” he said. “To put this in historical perspective, with the students who arrived in the fall of 2017, we placed 50th (five zero) amongst our Catholic peers.”

Schools like Fairfield often need to offer discounts to above-average students in the form of so-called merit aid to persuade them to matriculate. These discounts may have nothing to do with financial need. According to Fairfield’s most recent data, from the 2020-21 school year, it offered 89 percent of first-year, full-time students without financial need (who came from families with household incomes usually higher than $200,000) an average of $17,881 for their freshman year.

In a news release about the most recent first-year class, the school heralded the largest applicant pool ever. The release did not give a figure for Pell Grant recipients, though it did note that “numbers of first-generation students and students representing diverse populations” increased from the previous year.

President Nemec noted in his speech that “selectivity is not an end for us.” But it can create a kind of virtuous domino effect, and Fairfield is far from alone in using increased selectivity as a tactic to boost its standing and branding.

If all goes according to the playbook, better students will want to be with better students; rising selectivity will cause applications to increase without Fairfield having to spend ever more money on recruiting; more people will be willing to pay the list price to live and study there; donations will rise; and then there will be more money to recruit and support low-income students. It could work, but it would take many years.

Another possibility, however, is stagnant or declining percentages of Pell Grant recipients; low-income applicants wondering whether they may get a better deal elsewhere; and current students wondering how much the institution cares for people who are historically underrepresented. Fairfield did itself no favors this year when the administration ordered its mental-health counseling center to remove a “Black Lives Matter” banner from its window.

Eden Marchese, a senior who has worked in the admissions office and who is the director of diversity and inclusion for the Fairfield University Student Association, was not surprised by the school’s low Pell figure. Mx. Marchese was quick to note that there were college employees doing incredible work. Still, Mx. Marchese would offer qualified advice to prospective students considering the school.

“If you want to be a trailblazer, there is so much room for you to find yourself here,” Mx. Marchese said. “But there are also other places that can make you feel safer and can make you feel like you belong there. The senses of belonging here for me have been so few and far between, and it’s heartbreaking.”

The school told me, via email, that it did measure “belonging” through “retention, success and student satisfaction and engagement surveys.” I asked to see the results from Pell Grant recipients on satisfaction and engagement, but the school would not give them to me.

“As a first-generation Pell recipient and someone who identifies as coming from a diverse background, the university has been nothing but welcoming,” Mr. Unis, the enrollment vice president, said in an email.

Next year, the school plans to open Fairfield Bellarmine, in nearby Bridgeport. There, up to 100 “traditionally underrepresented” students will pursue two-year degrees in a program grounded in the liberal arts. Fairfield has a new full-tuition scholarship program at the main campus, too. This is a start.

Fairfield’s biggest challenge may be financial. It could spend more to recruit higher numbers of lower-income students and then discount tuition enough for the education to be affordable.

That could require budget cuts elsewhere, though, say from the dining hall or dorm remodeling. If you do that enough, higher-income families who already subsidize tuition for lower-income students may never even apply.

Make no mistake, this is a business, and the choices Fairfield faces are similar to ones that hundreds of other schools must make. College-shopping families and students could prioritize diversity over new buildings and amenities if they wanted to, but schools worry that most of them — most of us — do not and never will.

Wealthy alumni have choices to make, too. The lead gift on the new arena came from Shelagh Mahoney-McNamee, who is also a board member. She did not respond to several messages seeking comment on how she allocates her giving or whether she had considered other philanthropic options aside from the arena. She could consider them.

Fairfield has no shortage of people with expertise on Catholic teachings. Most of them did not reply to my inquiries about the godliness of a low Pell number. But Paul Lakeland, a professor and founding director of the school’s Center for Catholic Studies, was willing to weigh in.

He noted that the school “desperately” needed an arena of some sort. Then, he continued.

“You measure the common good of any community by the degree to which it prioritizes the needs of the least fortunate members,” he said. “A healthy community is one where the least fortunate are given the greatest attention.”