Classifications of Hecke Fields and Galois Images of Weight One Exotic Newforms

2025/08/30 by Ryotaro Sakamoto, Sakamoto, Ryotaro, Sho Yoshikawa +1
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.2509.00502

openalex publication_date 2025/08/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We determine the Hecke fields associated with weight one newforms of A₄-, S₄-, and A₅-type, expressed in terms of the order of its nebentypus. Furthermore, for each type, we provide a complete classification of the images of the corresponding Galois representations.

Citations

• An explicit upper bound for the least prime ideal in the Chebotarev\n density theorem
• A computation of modular forms of weight one and small level
• Finite subgroups of PGL(2,K)
• On the generation of the coefficient field of a newform by a single Hecke eigenvalue

Related

• On the generation of the coefficient field of a newform by a single Hecke eigenvalue
• Derived Hecke algebra for weight one forms
• Trace formulas of the Hecke operator on the spaces of newforms
• Decomposition theorems for Hilbert modular newforms
• Effective generation of Hecke algebras and explicit estimates of Sato--Tate type