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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 $f$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1402.0900","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2014-02-04T22:18:14Z","cross_cats_sorted":[],"title_canon_sha256":"c8d143a8011b608de355ac5281249b3ac0605981a143043f8df8539aa1861c9e","abstract_canon_sha256":"46fd06082b581d5f9379b34d2056843d6e8867e8422a29deb0d59d6839ed0bc7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:05.419295Z","signature_b64":"OcBEUd2yaKTuiU3AkzpW6THwbOWuDTXBCcZpj0r1UHQIBuVGrc1ZsltXf1ADt80ac0i+PnpWFz25+SOwJdrMDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0123338d97bacb81ef3e49176a9cc24b54c99d4171ac6efa84393b6e70063254","last_reissued_at":"2026-05-18T02:28:05.418743Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:05.418743Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1402.0900","created_at":"2026-05-18T02:28:05.418825+00:00"},{"alias_kind":"arxiv_version","alias_value":"1402.0900v2","created_at":"2026-05-18T02:28:05.418825+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.0900","created_at":"2026-05-18T02:28:05.418825+00:00"},{"alias_kind":"pith_short_12","alias_value":"AERTHDMXXLFY","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_16","alias_value":"AERTHDMXXLFYD3Z6","created_at":"2026-05-18T12:28:19.803747+00:00"},{"alias_kind":"pith_short_8","alias_value":"AERTHDMX","created_at":"2026-05-18T12:28:19.803747+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN","json":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN.json","graph_json":"https://pith.science/api/pith-number/AERTHDMXXLFYD3Z6JELWVHGCJN/graph.json","events_json":"https://pith.science/api/pith-number/AERTHDMXXLFYD3Z6JELWVHGCJN/events.json","paper":"https://pith.science/paper/AERTHDMX"},"agent_actions":{"view_html":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN","download_json":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN.json","view_paper":"https://pith.science/paper/AERTHDMX","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1402.0900&json=true","fetch_graph":"https://pith.science/api/pith-number/AERTHDMXXLFYD3Z6JELWVHGCJN/graph.json","fetch_events":"https://pith.science/api/pith-number/AERTHDMXXLFYD3Z6JELWVHGCJN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN/action/storage_attestation","attest_author":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN/action/author_attestation","sign_citation":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN/action/citation_signature","submit_replication":"https://pith.science/pith/AERTHDMXXLFYD3Z6JELWVHGCJN/action/replication_record"}},"created_at":"2026-05-18T02:28:05.418825+00:00","updated_at":"2026-05-18T02:28:05.418825+00:00"}