On vector-valued Siegel modular forms of degree 2 and weight (j,2)

2017/09/06 by Cléry, Fabien, van der Geer, Gerard
#Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1709.01748

Abstract

We formulate a conjecture that describes the vector-valued Siegel modular forms of degree 2 and level 2 of weight Sym^j det² and provide some evidence for it. We construct such modular forms of weight (j,2) via covariants of binary sextics and calculate their Fourier expansions illustrating the effectivity of the approach via covariants. Two appendices contain related results of Chenevier; in particular a proof of the fact that every modular form of degree 2 and level 2 and weight (j,1) vanishes.

Related

• Computations of vector-valued Siegel modular forms
• Siegel modular forms of genus 2 and level 2
• Constructing vector-valued Siegel modular forms from scalar-valued Siegel modular forms
• Basic vector valued Siegel modular forms of genus two
• Explicit computations of Siegel modular forms of degree two