Let W ⊂ ℝr be a lattice, and let deg : N → ℂ be a piecewise-linear function that is linear on the cones of a complete rational polyhedral fan. Under certain conditions on deg, the data (N, deg) determines a function f : Heng hooktop sign → ℂ that is a holomorphic modular form of weight r for the congruence subgroup Γ1(l). Moreover, by considering all possible pairs (N, deg), we obtain a natural subring Script T sign (l) of modular forms with respect to Γ1(l). We construct an explicit set of generators for Script T sign (l), and show that Script T sign (l) is stable under the action of the Hecke operators. Finally, we relate Script T sign (l) to the Hirzebruch elliptic genera that are modular with respect to Γ1(l).
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