Annales Mathematiques Du Quebec
In this computational paper we verify a truncated version of the Buzzard–Calegari conjecture on the Newton polygon of the Hecke operator T2 for all large enough weights. We first develop a formula for computing p-adic valuations of exponential sums, which we then implement to compute 2-adic valuations of traces of Hecke operators acting on spaces of cusp forms. Finally, we verify that if Newton polygon of the Buzzard–Calegari polynomial has a vertex at n≤15, then it agrees with the Newton polygon of T2 up to n.
This is a post-print originally published by Springer Nature, in Annales Mathematiques Du Quebec, October 2020. You can find the original version: https://doi.org/10.1007/s40316-020-00149-z
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Chiriac, L., & Jorza, A. (2020). Newton polygons of Hecke operators. Annales Mathématiques Du Québec. https://doi.org/10.1007/s40316-020-00149-z