Hecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$

Giovanna De Lauri; Dan Fretwell

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arXiv · 2610.13295

Hecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$

Giovanna De Lauri·Dan Fretwell

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Abstract

We consider Hecke modules of orthogonal modular forms attached to definite ternary lattices of half-discriminant $p^2$ with $p$ prime and $4p^2$ with $p$ an odd prime. Where possible, we prove explicit Jacquet-Langlands style correspondences with spaces of classical modular forms (in the spirit of Birch and Hein-Tornaria-Voight), and give conjectures for the remaining genera. This is done by applying sequences of Watson-style transformations that reduce the discriminant while preserving the adelic orthogonal group.

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BibTeX RIS

Giovanna De Lauri, Dan Fretwell. 2026-10-09. Hecke modules associated to certain ternary lattices of half-discriminant $p^2$ and $4p^2$. https://arxiv.org/abs/2610.13295

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