{"paper":{"title":"A space of weight one modular forms attached to totally real cubic number fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Guillermo Mantilla-Soler","submitted_at":"2011-09-10T19:07:34Z","abstract_excerpt":"Let $d$ be a positive fundamental discriminant, and let $\\mathcal{C}_{d}$ be the set of isomorphism classes of cubic number fields of discriminant $d$. For each $K \\in \\mathcal{C}_{d}$, we construct a weight 1 modular form $f_{K}$ with level $3^{\\pm 1}d$ and nebentypus $\\left( \\frac{-3^{\\pm 1}d}{\\cdot} \\right)$. We show that the form $f_{K}$ completely determines the field $K$. Moreover, we show that $\\{f_{K} : K \\in \\mathcal{C}_{d}\\}$ is a linearly independent set."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1109.2251","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"}