{"paper":{"title":"On the norms of $p$-stabilized elliptic newforms (with an appendix by Keith Conrad)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Jim Brown, Krzysztof Klosin","submitted_at":"2014-02-04T22:18:14Z","abstract_excerpt":"Let $f \\in S_{\\kappa}(\\Gamma_0(N))$ be a Hecke eigenform at $p$ with eigenvalue $\\lambda_f(p)$ for a prime $p$ not dividing $N$. Let $\\alpha_p$ and $\\beta_p$ be complex numbers satisfying $\\alpha_p + \\beta_p = \\lambda_f(p)$ and $\\alpha_p \\beta_p = p^{\\kappa-1}$. We calculate the norm of $f_{p}^{\\alpha_p}(z) = f(z) - \\beta_{p} f(pz)$ as well as the norm of $U_p f$, both classically and adelically. We use these results along with some convergence properties of the Euler product defining the symmetric square L-function of $f$ to give a `local' factorization of the Petersson norm of $f$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.0900","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"}