Hermitian modular forms and algebraic modular forms on $SO(6)$

TL;DR

This paper explores conjectural links between Hermitian modular forms of degree two and algebraic modular forms on SO(6), supported by dimension formulas and explicit eigenform computations.

Contribution

It proposes conjectures connecting two types of modular forms and provides evidence through formulas and computational examples.

Findings

Dimension formulas for modular forms

Explicit eigenform computations

Support for conjectural relationships

Abstract

We state conjectures that relate Hermitian modular forms of degree two and algebraic modular forms for the compact group $SO(6)$. We provide evidence for these conjectures in the form of dimension formulas and explicit computations of eigenforms.