Abstract
We extend Igusa’s description of the relation between invariants of binary sextics and Siegel modular forms of degree 2 to a relation between covariants and vector-valued Siegel modular forms of degree 2. We show how this relation can be used to effectively calculate the Fourier expansions of Siegel modular forms of degree 2.
Highlights
Mathematics Subject Classification 10D · 11F11 · 14L24 · 13A50. In his 1960 papers Igusa explained the relation between the invariant theory of binary sextics and scalar-valued Siegel modular forms of degree 2
We show that our constructions can be used to efficiently calculate the Fourier expansions of vector-valued Siegel modular forms
We will denote by Sym6(V ) the space of binary sextics, where we write a binary sextic as f = ai i =0
Summary
In his 1960 papers Igusa explained the relation between the invariant theory of binary sextics and scalar-valued Siegel modular forms of degree (or genus) 2. The relation stems from the fact that the moduli space M2 of curves of genus 2 admits two descriptions. The moduli space M2 has a classical description in terms of the invariant theory
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