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The resulting density agrees with the one previously obtained for odd conductor exponents, and hence gives a uniform density for cusp forms of conductor $\\ell^n$ as $n\\to\\infty$. We also consider the case of Maass forms of conductor $\\ell^n$. Finally, we compute the murmuration density in cond"},"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":"2606.08353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2026-06-06T21:56:01Z","cross_cats_sorted":[],"title_canon_sha256":"ed2bf9bc1973ddb9bef0e759a116fb6ac25c9d026f3679db2457daa8f483774e","abstract_canon_sha256":"19f84586d3fdce469ac18b78ff6164199fe8614fd515a379442b3612538c47de"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-09T01:05:34.467472Z","signature_b64":"8vrnIYxFuLxMS/qu0GCvoJV0+NM1MKJyJ9duOS3YA3LUFuZ5eYob1BMJFFFfOAi8jJINGhwD2HK8Q72ttmKYCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"14d6817b9a5b1eb571fee623e35fc99e96f2c6c83a48a1b66c6ec959088cf9cb","last_reissued_at":"2026-06-09T01:05:34.467045Z","signature_status":"signed_v1","first_computed_at":"2026-06-09T01:05:34.467045Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Murmurations in the Depth Aspect for Maass and Modular Forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Leonard Tomczak","submitted_at":"2026-06-06T21:56:01Z","abstract_excerpt":"We study murmurations in the depth aspect for holomorphic cusp forms of conductor $\\ell^{2a}$ and fixed weight, where $\\ell$ is an odd prime. 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