Supercuspidal ramification of modular endomorphism algebras

Bhattacharya, Shalini; Ghate, Eknath

doi:10.1090/proc/12629

Supercuspidal ramification of modular endomorphism algebras
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by Shalini Bhattacharya and Eknath Ghate

Proc. Amer. Math. Soc. 143 (2015), 4669-4684

DOI: https://doi.org/10.1090/proc/12629

Published electronically: May 7, 2015

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Abstract:

The endomorphism algebra $X_f$ attached to a non-CM primitive cusp form $f$ of weight at least two is a 2-torsion element in the Brauer group of a number field $F$. We give formulas for the ramification of $X_f$ locally at primes lying above the odd supercuspidal primes of $f$. We show that the local Brauer class is determined by the underlying local Galois representation together with an auxiliary Fourier coefficient.

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