{"paper":{"title":"Balanced modular parameterizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Danny Lara, Esteban Melendez, Tim Huber","submitted_at":"2014-05-27T00:23:11Z","abstract_excerpt":"For prime levels $5 \\le p \\le 19$, sets of $\\Gamma_{0}(p)$-permuted theta quotients are constructed that generate the graded rings of modular forms of positive integer weight for $\\Gamma_{1}(p)$. An explicit formulation of the permutation representation and several applications are given, including a new representation for the number of $t$-core partitions. The $\\Gamma_{0}(p)$-action induces coefficient symmetries within representations for modular forms and invariance subgroups for coupled systems of differential equations. The symmetry for levels $p = 5,7,11$ is linked to the Kleinian automo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.6761","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"}