Computing Genus-2 Hilbert–Siegel Modular Forms over via the Jacquet–Langlands Correspondence

In this paper we present an algorithm for computing Hecke eigensystems of Hilbert–Siegel cusp forms over real quadratic fields of narrow class number one. We give some illustrative examples using the quadratic field . In those examples, we identify Hilbert–Siegel eigenforms that are possible lifts from Hilbert eigenforms.