{"paper":{"title":"Generators and relations for the shallow mod 2 Hecke algebra in levels $\\Gamma_{0}(3)$ and $\\Gamma_{0}(5)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Paul Monsky","submitted_at":"2017-03-12T23:05:05Z","abstract_excerpt":"Let $M(\\mathit{odd})\\subset Z/2[[x]]$ be the space of odd mod~2 modular forms of level $\\Gamma_{0}(3)$. It is known that the formal Hecke operators $T_{p}:Z/2[[x]]\\rightarrow Z/2[[x]]$, $p$ an odd prime other than $3$, stabilize $M(\\mathit{odd})$ and act locally nilpotently on it. So $M(\\mathit{odd})$ is an $\\mathcal{O} = Z/2[[t_{5},t_{7}, t_{11}, t_{13}]]$-module with $t_{p}$ acting by $T_{p}$, $p\\in \\{5,7,11,13\\}$. We show:\n  (1) Each $T_{p}:M(\\mathit{odd})\\rightarrow M(\\mathit{odd})$, $p\\ne 3$, is multiplication by some $u$ in the maximal ideal, $m$, of $\\mathcal{O}$.\n  (2) The kernel, $I$,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04193","kind":"arxiv","version":1},"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"}