Covariants of binary sextics and vector-valued Siegel modular forms of genus two

TL;DR

This paper extends Igusa's classical work by establishing a link between covariants of binary sextics and vector-valued Siegel modular forms of genus two, enabling efficient computation of their Fourier expansions.

Contribution

It introduces a novel relation between covariants and vector-valued Siegel modular forms, enhancing computational methods for these forms.

Findings

Established a new relation between covariants and modular forms.

Enabled effective calculation of Fourier expansions.

Extended Igusa's classical invariant theory to vector-valued forms.

Abstract

We extend Igusa's description of the relation between invariants of binary sextics and Siegel modular forms of degree two to a relation between covariants and vector-valued Siegel modular forms of degree two. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree two.