Atkin-Lehner Decompositions for Quaternionic modular forms
Number Theory
2025-11-13 v2 Representation Theory
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.
Cite
@article{arxiv.2511.06584,
title = {Atkin-Lehner Decompositions for Quaternionic modular forms},
author = {Siddharth Ramakrishnan Cherukara},
journal= {arXiv preprint arXiv:2511.06584},
year = {2025}
}