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Honda and Kaneko proved infinite families of congruences of the form $f|U(p) \\equiv 0 \\pmod{p}$ for weakly holomorphic modular forms of low weight and level and primes $p$ in certain residue classes, and conjectured the existence of similar congruences modulo higher powers of $p$. Partial results on some of these conjectures were proved recently by Guerzhoy. We construct infinite families of weakly holomorphic modular forms on the Fricke groups $\\Gamma^*(N)$ for $N=1,2,3,4$ and describe explicitly the action of the Hecke algebra on these"},"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":"1305.7455","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2013-05-31T15:34:20Z","cross_cats_sorted":[],"title_canon_sha256":"ed8f92e2ea919e50120e9df426b0f492cd6ef35cc2cd77896ef0541c9c67dda5","abstract_canon_sha256":"18cb98efbacd9b24403105c6698db11b7a7123e3beb2d602b8f87a6d36017e17"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:18:52.062039Z","signature_b64":"1Uq3SgBxMV63ivE0fLLIjJ5LILHeLGDRvlPJUCZLsMAtPulYyvDZ5whPP8192YE2H2NkjBZV3rqdZDgaWsWQCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cfcaf684b21c845cb7852e6fe2fe3c641073a58615128a9053575f3021880702","last_reissued_at":"2026-05-18T02:18:52.061409Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:18:52.061409Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Hecke grids and congruences for weakly holomorphic modular forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Nickolas Andersen, Scott Ahlgren","submitted_at":"2013-05-31T15:34:20Z","abstract_excerpt":"Let $U(p)$ denote the Atkin operator of prime index $p$. 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