Computation of weight 1 modular forms with exotic representations

2022/01/21 by Kieran Child, Child, Kieran
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2201.08873

openalex publication_date 2022/01/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a deterministic algorithm for computing spaces of weight 1 modular forms with exotic representations. This algorithm is an improved version of Schaeffer's Hecke stability method, utilising the author's previous work on the twist-minimal trace formula for weight 2 holomorphic forms, and presenting a method of lifting forms from characteristic p. The algorithm was used to compute all such forms with level at most 10,000. Together with Sutherland's computation of dihedral forms, this allows us to present the dimensions of all weight 1 newform spaces up to level 10,000.

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