{"paper":{"title":"A Hecke algebra attached to mod 2 modular forms of level 3","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2015-08-30T02:04:00Z","abstract_excerpt":"Let $D$ in $Z/2[[x]]$ be $\\sum x^{n^{2}}$, $n>0$ and prime to $6$. Let $W$ be spanned by the $D^{k}$, $k>0$ and prime to $6$. Then the formal Hecke operators $T_{p}$, $p>3$, stabilize $W$, and it can be shown that they act locally nilpotently. We show that the completion of the Hecke algebra generated by these $T_{p}$ acting on $W$, with respect to the maximal ideal generated by the $T_{p}$, is a power series ring in $T_{7}$ and $T_{13}$ with an element of square $0$ adjoined. This may be viewed as a level 3 analog of the level 1 results of Nicolas and Serre -- the Hecke stable space they stud"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.07523","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":""},"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"}