Harmonic theta series and the Kodaira dimension of ${\mathcal{A}}_6$

Abstract

We construct a basis of the space ${\text{S}}_{14}({\text{Sp}}_{12}(\mathbb{Z}))$ of Siegel cusp forms of degree $6$ and weight $14$ consisting of harmonic theta series. One of these functions has vanishing order $2$ at the boundary which implies that the Kodaira dimension of ${\mathcal{A}}_6$ is non-negative.