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In this paper, we describe an algorithm for computing algebraic modular forms on compact inner forms of      G S p 4 \mathrm {GSp}_4       over totally real number fields. By analogues of the Jacquet-Langlands correspondence for      G L 2 \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 ( 2 ) \mathbb {Q}(\sqrt {2})      .

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