In a previous paper , we defined the space of toric forms T.l., and showed that it is a finitely generated subring of the holomorphic modular forms of integral weight on the congruence group G1.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 ; 1.30. The proof uses work of Merel, and involves an explicit computation of the intersection pairing on Manin symbols.
All Science Journal Classification (ASJC) codes
- Applied Mathematics