{"paper":{"title":"A note on the dimension of the largest simple Hecke submodule","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Corentin Perret-Gentil, Maksym Radziwi{\\l}{\\l}, Sandro Bettin","submitted_at":"2018-10-03T23:27:35Z","abstract_excerpt":"For $k\\ge 2$ even, let $d_{k,N}$ denote the dimension of the largest simple Hecke submodule of $S_{k}(\\Gamma_0(N); \\mathbb{Q})^\\text{new}$. We show, using a simple analytic method, that $d_{k,N} \\gg_k \\log\\log N / \\log(2p)$ with $p$ the smallest prime co-prime to $N$. Previously, bounds of this quality were only known for $N$ in certain subsets of the primes. We also establish similar (and sometimes stronger) results concerning $S_{k}(\\Gamma_0(N), \\chi)$, with $k \\geq 2$ an integer and $\\chi$ an arbitrary nebentypus."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.02006","kind":"arxiv","version":3},"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"}