Computing Hilbert modular forms as orthogonal modular forms

2025/06/27 by Hein, Jeffery, Tornaria, Gonzalo, Voight, John
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.21981

Abstract

We show how to efficiently compute Hilbert modular forms as orthogonal modular forms, generalizing and expanding upon the method of Birch.

Citations

• Definite orthogonal modular forms: Computations, Excursions and Discoveries
• Quinary forms and paramodular forms
• Computing newforms using supersingular isogeny graphs
• On the Lattice Isomorphism Problem
• Lattice methods for algebraic modular forms on classical groups
• Explicit methods for Hilbert modular forms
• Identifying the matrix ring: algorithms for quaternion algebras and quadratic forms
• Characterizing quaternion rings over an arbitrary base

Related

• Hilbert modular forms and their applications
• Hilbert modular forms and Galois representations
• Explicit Methods for Hilbert Modular Forms of Weight 1
• A database of Hilbert modular forms
• Explicit methods for Hilbert modular forms