{"paper":{"title":"On l-adic representations for a space of noncongruence cuspforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Helena Verrill, Jerome W. Hoffman, Ling Long","submitted_at":"2010-03-19T15:10:21Z","abstract_excerpt":"This paper is concerned with a compatible family of 4-dimensional \\ell-adic representations \\rho_{\\ell} of G_\\Q:=\\Gal(\\bar \\Q/\\Q) attached to the space of weight 3 cuspforms S_3 (\\Gamma) on a noncongruence subgroup \\Gamma \\subset \\SL. For this representation we prove that: 1.)It is automorphic: the L-function L(s, \\rho_{\\ell}^{\\vee}) agrees with the L-function for an automorphic form for \\text{GL}_4(\\mathbb A_{\\Q}), where \\rho_{\\ell}^{\\vee} is the dual of \\rho_{\\ell}. 2.) For each prime p \\ge 5 there is a basis h_p = \\{h_p ^+, h_p ^- \\} of S_3 (\\Gamma) whose expansion coefficients satisfy 3-te"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.3808","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"}