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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, $I$,","authors_text":"Paul Monsky","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-12T23:05:05Z","title":"Generators and relations for the shallow mod 2 Hecke algebra in levels $\\Gamma_{0}(3)$ and $\\Gamma_{0}(5)$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04193","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a526671c6e942788ad319f32fc454eeba394a3a2f925fdac626a5d439d16ba43","target":"record","created_at":"2026-05-18T00:48:49Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"1289057fe4eb2d573675e50c12eda4452da186c904cddca43f3ba0c55df7b1a5","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-03-12T23:05:05Z","title_canon_sha256":"98ff0c0489084700952af3561de8aa867ed3e7b771018d4512719f444d4f59ca"},"schema_version":"1.0","source":{"id":"1703.04193","kind":"arxiv","version":1}},"canonical_sha256":"92ba079a4b41c351300a4844cbf2b0868d955cf2a5a1d21d6fdec5aeafb832b8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"92ba079a4b41c351300a4844cbf2b0868d955cf2a5a1d21d6fdec5aeafb832b8","first_computed_at":"2026-05-18T00:48:49.504865Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:48:49.504865Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Fn1MMKm/LPu/gPji/686czDTx6UqaltNWrXWHJDpeQ+644y7bkD7BPKDTANBELUmNJZm176g0S6MvCiOLBytBw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:48:49.505661Z","signed_message":"canonical_sha256_bytes"},"source_id":"1703.04193","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a526671c6e942788ad319f32fc454eeba394a3a2f925fdac626a5d439d16ba43","sha256:7dbf7cd376523c9f060a6a16ef533a21e933c9511ed0c52f95af50459218a3d1"],"state_sha256":"f488c824af23e0d64ae794e830fd56aa3a181c36115f6f14d98ec46926a3aea7"}