Congruences Between Systems of Eigenvalues of Modular Forms

Naomi Jochnowitz
1982 Transactions of the American Mathematical Society  
We modify and generalize proofs of Täte and Serre in order to show that there are only a finite number of systems of eigenvalues for the Hecke operators with respect to T0( N) mod /. We also summarize results for r,(/V). Using these results, we show that an arbitrary prime divides the discriminant of the classical Hecke ring to a power which grows linearly with k. In this way, we find a lower bound for the discriminant of the Hecke ring. After limiting ourselves to cusp forms, we also find an
more » ... per bound. Lastly we use the constructive nature of Täte and Serre's result to describe the structure and dimensions of the generalized eigenspaces for the Hecke operators mod /.
doi:10.2307/1999772 fatcat:yn7za2v2lfgxhknacvxvsowsvq