ON THE COMPUTATION OF ALGEBRAIC MODULAR FORMS ON COMPACT INNER FORMS OF GSp4

摘要

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 genus2. We give some examples of such eigensystems over Q(√2).