Toric modular forms of higher weight

In two previous papers we used the geometry of complete polyhedral fans to construct a subring $\text{TTT}(l)$ of the modular forms on ${\mathrm{\Gamma }}_1(l)$, and showed that for weight two the cuspidal part of $\text{TTT}(l)$ 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 $\text{TTT}(l)$ coincides with the space of all cusp forms.