Preston Wake

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20242026

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math.NT2026

Counting level-raising congruences using modular representation theory

Jaclyn Lang, Robert Pollack, Preston Wake

We introduce a new method for studying mod- $ℓ$ congruences between eigenforms through the modular representation theory of $PGL_{2} (F_{p})$ . When $p\equiv \pm 1 \p…

math.NT2025

Modular analogs of character formulas and minimal lifts of modular forms

Patrick B. Allen, Preston Wake

If $f$ is a mod- $3$ eigenform of weight 2 and level $Γ_{0} (ℓ^{2})$ for a prime $ℓ$ such that $ℓ \equiv - 1 (mod 3)$ , and $ℓ$ is a vexing prime for $f$ , we show that there i…

math.NT2024

Iwasawa invariants in residually reducible Hida families

Robert Pollack, Preston Wake

We study the variation of $μ$ -invariants of modular forms in a cuspidal Hida family in the case that the family intersects an Eisenstein family. We allow for intersections that occ…