Wednesday, April 12, 2017 - 2:30pm
This talk will focus on polynomial identities between Hecke eigenforms. In particular we will show that assuming Maeda's conjecture, then all solutions to the equation X^2=\sum a_iY_i in terms of Hecke eigenforms for SL_2(Z) are forced by dimension considerations. Our proof uses Galois theory for the eigenvalues of the Hecke operators acting the space of cusp forms for SL_2(Z). We will also talk about how this is related with nonvanishing of certain L-series and the case for the congruence subgroups.