Adjoint lifts and modular endomorphism algebras

Abstract

We prove that the ramification of the endomorphism algebra of the Grothendieck motive attached to a non-CM cuspform of weight two or more is completely determined by the slopes of the adjoint lift of this form, when the slopes are finite. We treat all places of good and bad reduction, answering a question of Ribet about the Brauer class of the endomorphism algebra in the finite slope case.