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-Livnè. It also generalizes a construction of Scholl to indefinite division quaternion algebras, and provides the first motivic construction of new-subspaces of modular forms.
Dirac operators in tensor categories and the motive of quaternionic modular forms / M. Masdeu, M.A. Seveso. - In: ADVANCES IN MATHEMATICS. - ISSN 0001-8708. - 313(2017 Jun), pp. 628-688. [10.1016/j.aim.2017.03.034]
Dirac operators in tensor categories and the motive of quaternionic modular forms
M.A. Seveso
2017
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-Livnè. It also generalizes a construction of Scholl to indefinite division quaternion algebras, and provides the first motivic construction of new-subspaces of modular forms.
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