{"paper":{"title":"Modular analogs of character formulas and minimal lifts of modular forms","license":"http://creativecommons.org/licenses/by-nc-nd/4.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Patrick B. Allen, Preston Wake","submitted_at":"2025-09-25T11:21:36Z","abstract_excerpt":"If $f$ is a mod-$3$ eigenform of weight 2 and level $\\Gamma_0(\\ell^2)$ for a prime $\\ell$ such that $\\ell \\equiv -1 \\pmod{3}$, and $\\ell$ is a vexing prime for $f$, we show that there is no obstruction to finding a minimal lift of $f$, but that there is an obstruction to finding a nonminimal lift. The key new ingredient that we prove is a modular analog of the standard character formula for a cuspidal representation of $\\mathrm{GL}_2(\\mathbb{F}_\\ell)$, an enhancement that allows us to easily compute the group cohomology of a $3$-adic lattice in such a representation. In fact, we provide a gene"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2509.21426","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2509.21426/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}