On the computation of algebraic modular forms on compact inner forms of GSp₄

2009/12/06 by Lassina Dembélé, Dembele, Lassina
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.0912.1145

openalex publication_date 2009/12/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we describe an algorithm for computing algebraic modular forms on compact inner forms of GSp₄ over totally real number fields. By analogues of the Jacquet-Langlands correspondence for GL₂, this algorithm in fact computes Hecke eigensystems of Hilbert-Siegel modular forms of genus 2. We give some examples of such eigensystems over \Q(√(2)).

Related

• Computing genus 2 Hilbert-Siegel modular forms over \Q(√(5)) via the Jacquet-Langlands correspondence
• Explicit methods for Hilbert modular forms
• Computing systems of Hecke eigenvalues associated to Hilbert modular\n forms
• Siegel modular forms (mod p) and algebraic modular forms
• Hecke eigenvalues of Siegel modular forms (mod p) and of algebraic modular forms