{"paper":{"title":"Images of Pseudo-Representations and Coefficients of Modular Forms modulo p","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jo\\\"el Bella\\\"iche","submitted_at":"2015-05-05T23:08:14Z","abstract_excerpt":"We describe the image of general families of two-dimensional representations over compact semi-local rings. Applying this description to the family carried by the universal Hecke algebra acting on the space of modular forms of level $N$ modulo a prime $p$, we prove new results about the coefficients of modular forms mod $p$. If $f=\\sum_{n=0}^\\infty a_n q^n$ is such a form, for which we can assume without loss of generality that $a_n=0$ if $(n,Np)>1$, calling $\\delta(f)$ the density of the set of primes $\\ell$ such that $a_\\ell \\neq 0$, we prove that $\\delta(f)>0$ provided that $f$ is not zero "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1505.01216","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"}