Generators for modules of vector-valued Picard modular forms

TL;DR

This paper constructs generators for modules of vector-valued Picard modular forms on a specific unitary group and computes eigenvalues of Hecke operators on cusp forms, advancing understanding of their algebraic and arithmetic properties.

Contribution

It introduces explicit generators for modules of vector-valued Picard modular forms and calculates Hecke eigenvalues, providing new tools for studying these automorphic forms.

Findings

Explicit generators for modules of vector-valued Picard modular forms.

Eigenvalues of Hecke operators on cusp forms are computed.

Enhanced understanding of the structure and arithmetic of Picard modular forms.

Abstract

We construct generators for modules of vector-valued Picard modular forms on a unitary group of type (2,1) over the Eisenstein integers. We also calculate eigenvalues of Hecke operators acting on cusp forms.