Thackeray 427

### Abstract or Additional Information

Given a Hilbert modular form *f* over a totally real field *F*, we can associate to it a finite module *P(f)* known as the __congruence module__ for *f*, which measures the congruences that *f* satisfies with other forms. When *f* is transferred to a quaternionic modular form *f _{D}* over a quaternion algebra

*D*(via the Jacquet-Langlands correspondence), we can similarly define a congruence module

*P(f*for

_{D})*f*. Pollack and Weston proposed a quantitative relationship between the sizes of

_{D}*P(f)*and

*P(f*, expressed in terms of invariants associated to

_{D})*f*and

*D*.

In this talk, I will present the proof of this relationship under some hypotheses. The proof combines a generalization of a result of Ribet and Takahashi with new techniques introduced by Böckle, Khare, and Manning.