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arXiv · 2511.06584

Atkin-Lehner Decompositions for Quaternionic modular forms

Siddharth Ramakrishnan Cherukara
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Abstract

In this paper, we obtain Atkin--Lehner decompositions for spaces of modular forms on definite quaternion algebras. Similar to Casselman's approach our methods are representation theoretic. Using Jacquet--Langlands correspondence we also obtain isomorphisms between spaces of quaternionic modular forms and corresponding spaces of Hilbert modular forms.

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Siddharth Ramakrishnan Cherukara. 2025-11-10. Atkin-Lehner Decompositions for Quaternionic modular forms. https://arxiv.org/abs/2511.06584

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