Dirac operators in tensor categories and the motive of quaternionic modular forms

Abstract

We define a motive whose realizations afford modular forms (of arbitrary weight) on an indefinite division quaternion algebra. This generalizes work of Iovita--Spiess to odd weights in the spirit of Jordan--Livné. It also generalizes a construction of Scholl to indefinite division quaternion algebras.

arXiv comment39 pages. Final revised version with slight title modification, to appear in: "Advances in Mathematics"