{"paper":{"title":"A Note On Non-ordinary Primes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Ken Ono, Seokho Jin, Wenjun Ma","submitted_at":"2015-11-20T19:04:52Z","abstract_excerpt":"Suppose that $O_L$ is the ring of integers of a number field $L$, and suppose that $f(z)=\\sum_{n=1}^\\infty a_f(n)q^n\\in S_k\\cap O_L[[q]]$ (note: $q := e^{2\\pi iz}$) is a normalized Hecke eigenform for $\\mathrm{SL}_2(\\mathbb{Z})$. We say that $f$ is non-ordinary at a prime $p$ if there is a prime ideal $\\mathfrak{p}\\subset O_L$ above $p$ for which $a_f(p)\\equiv 0 \\ (mod\\ {\\mathfrak{p}})$. For any finite set of primes $S$, we prove that there are normalized Hecke eigenforms which are non-ordinary for each $p\\in S$. The proof is elementary and follows from a generalization of work of Choie, Kohne"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.06725","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"}