Preston Wake

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math.NT2026

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 $I^_{0} (ℓ^{2})$ for a prime $ℓ$ such that $ℓ \equiv - 1 (mod 3)$ , and $ℓ$ is a vexing prime for $f$ , we show that there…

math.NT2024

Iwasawa invariants in residually reducible Hida families

Robert Pollack, Preston Wake

We study the variation of $I^¼$ -invariants of modular forms in a cuspidal Hida family in the case that the family intersects an Eisenstein family. We allow for intersections that oc…