Seminar des SFB/TRR 326 GAUSCounting Congruences Between Modular Forms

For a given eigenform, how many other eigenforms of the same weight and level are congruent to it modulo a prime l? We will explain how modular representation theory can be used to help answer this question. We focus especially on the case when the level is the square of a prime p such that p = -1 mod l. This is ongoing joint work with Robert Pollack and Preston Wake.