Computing genus 2 Hilbert-Siegel modular forms over $\Q(\sqrt{5})$ via the Jacquet-Langlands correspondence

Details Computing genus 2 Hilbert-Siegel modular forms over $\Q(\sqrt{5})$ via the Jacquet-Langlands correspondence Computing genus 2 Hilbert-Siegel modular forms over $\Q(\sqrt{5})$ via the Jacquet-Langlands correspondence

2007-03-31

arxiv.org/abs/0704.0011v3

Mathematics

Number Theory

14 pages; title changed; to appear in Experimental Mathematics

Scientific paper

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
$\Q(\sqrt{5})$. In those examples, we identify Hilbert-Siegel eigenforms that
are possible lifts from Hilbert eigenforms.

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