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

Dembélé, Lassina

doi:10.1090/S0025-5718-2014-02374-0

On the computation of algebraic modular forms on compact inner forms of $\mathbf {GSp}_4$
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Abstract:

In this paper, we describe an algorithm for computing algebraic modular forms on compact inner forms of $\mathrm {GSp}_4$ over totally real number fields. By analogues of the Jacquet-Langlands correspondence for $\mathrm {GL}_2$, this algorithm in fact computes Hecke eigensystems of Hilbert-Siegel modular forms of genus 2. We give some examples of such eigensystems over $\mathbb {Q}(\sqrt {2})$.

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