Eigenspaces of Newforms with Nontrivial Character

2023/07/15 by Markos Karameris, Karameris, Markos
Computer Science · Mathematics · #11F11 #11F25 #11F33 #20C08 #FOS: Mathematics #Mathematical Dynamics and Fractals #Mathematics and Applications #Number Theory (math.NT) #Optimization and Variational Analysis #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2307.07804

openalex publication_date 2023/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let S_k(Γ₀(N),χ) denote the space of holomorphic cuspforms with Dirichlet character χ and modular subgroup Γ₀(N). We will characterize the space of newforms S_k^new(Γ₀(N),χ) as the intersection of eigenspaces of a particular family of Hecke operators, generalizing the work of Baruch-Purkait to forms with non-trivial character. We achieve this by obtaining representation theoretic results in the p-adic case which we then de-adelizize into relations of classical Hecke operators.

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