### Toric modular forms and nonvanishing of L-functions, by Lev A. Borisov and Paul E. Gunnells

In a previous paper, we defined the space of toric forms, and showed
that it is a finitely generated subring of the holomorphic modular
forms of integral weight on the congruence group Gamma_1(*l*).
In this article we prove the following theorem: modulo Eisenstein
series, the weight two toric forms coincide exactly with the vector
space generated by all cusp eigenforms *f* such that
*L*(*f*,1) is nonzero. The proof uses work of Merel, and
involves an explicit computation of the intersection pairing on Manin
symbols.

Lev A. Borisov and Paul E. Gunnells <lborisov@math.columbia.edu,gunnells@math.columbia.edu>