Toric modular forms of higher weight

Toric modular forms of higher weight Title: Toric modular forms of higher weight
Authors: Lev A. Borisov and Paul E. Gunnells

Abstract: In the papers \cite{vanish, toric} we used the geometry of complete polyhedral fans to construct a subring $\TTT (l)$ of the modular forms on $\Gamma _{1} (l)$, and showed that for weight two the cuspidal part of $\TTT (l)$ coincides with the space of cusp forms of analytic rank zero. In this paper we show that in weights greater than two, the cuspidal part of $\TTT (l)$ coincides with the space of all cusp forms.