Modular endomorphism algebras at super cuspidal primes

Let $f$ be a primitive non-CM cusp form of weight two or more. The endomorphism algebra X_f (attached to f) is a 2-torsion element in the Brauer group of some number field. We give a formula for the ramification of X_f locally for all places lying above super cuspidal primes. For p=2, we also treat the interesting case where the image of the Weil-Deligne representation attached to f is an exceptional group. This is a joint work with my student Tathagata Mandal.