{"paper":{"title":"Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ariel Pacetti, Jose Ignacio Burgos Gil","submitted_at":"2013-10-25T17:55:41Z","abstract_excerpt":"In this article we give an analogue of Hecke and Sturm bounds for Hilbert modular forms over real quadratic fields. Let $K$ be a real quadratic field and $\\Om_K$ its ring of integers. Let $\\Gamma$ be a congruence subgroup of $\\SL_2(\\Om_K)$ and $M_{(k_1,k_2)}(\\Gamma)$ the space of Hilbert modular forms of weight $(k_1,k_2)$ for $\\Gamma$. The first main result is an algorithm to construct a finite set $S$, depending on $K$, $\\Gamma$ and $(k_1,k_2)$, such that if the Fourier expansion coefficients of a form $G \\in M_{(k_1,k_2)}(\\Gamma)$ vanish on the set $S$, then $G$ is the zero form. The second"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.6991","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"}