{"paper":{"title":"Generators and relations of the graded algebra of modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nadim Rustom","submitted_at":"2014-02-03T15:48:26Z","abstract_excerpt":"We give bounds on the degree of generators for the ideal of relations of the graded algebras of modular forms with coefficients in $\\mathbb{Q}$ over congruence subgroups $\\Gamma_0(N)$ for $N$ satisfying some congruence conditions and for $\\Gamma_1(N)$. We give similar bounds for the graded $\\mathbb{Z}[\\frac{1}{N}]$-algebra of modular forms on $\\Gamma_1(N)$ with coefficients in $\\mathbb{Z}[\\frac{1}{N}]$. For a prime $p \\geq 5$, we give a lower bound on the highest weight appearing in a minimal list of generators for $\\Gamma_0(p)$, and we identify a set of generators for the graded algebra $M(\\G"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0405","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"}