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

Details On the computation of algebraic modular forms on compact inner forms of $\mathrm{GSp}_4$ On the computation of algebraic modular forms on compact inner forms of $\mathrm{GSp}_4$

2009-12-06

arxiv.org/abs/0912.1145v1

Mathematics

Number Theory

Scientific paper

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 $\Q(\sqrt{2})$.

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