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

Abstract

We construct a basis of the space $S_{14}\left({Sp}_{12}\left(\mathbb{Z}\right)\right)$ 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 nonnegative.