Hilbert modular forms of even weight and trivial character can be computed as orthogonal modular forms, with all Atkin-Lehner eigenspaces captured by a radical character.
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Computing Hilbert modular forms as orthogonal modular forms
Hilbert modular forms of even weight and trivial character can be computed as orthogonal modular forms, with all Atkin-Lehner eigenspaces captured by a radical character.