{"paper":{"title":"Joint level-weight murmurations for holomorphic newforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Julien Cardi","submitted_at":"2026-07-09T23:11:15Z","abstract_excerpt":"We establish an unconditional joint level-weight murmuration law for holomorphic newforms of squarefree level. The level N is averaged at size X, the even weight k at size K, and primes are measured in the coordinate p divided by N times ((k-1)/(4 pi)) squared. After normalization, the root-number weighted prime trace converges to a locally finite measure supported on rational squares, with explicitly given Euler-product masses. The convergence is uniform for X^epsilon <= K <= X^(1-epsilon), and therefore holds for K = X^rho for every fixed 0 < rho < 1. Starting from the exact trace formula, w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.08982","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2607.08982/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}