Lifting ethereal Bianchi modular forms

Abstract: Mod $p$ Hecke eigenforms for congruence subgroups of $\SL_2(\Z)$ which do not lift to characteristic $0$ have received much attention, and were named "ethereal modular forms" by G. Schaeffer. In this talk, we discuss liftability for mod $p$ Bianchi modular forms: experiments suggest that lifting to characteristic zero may always be possible by increasing the level, as in the case of classical modular forms. This is supported by some theoretical observations, including a proof of lifting in very special cases via recent advances by Caraiani-Newton on the modularity of elliptic curves over imaginary quadratic fields, as well as extensive computations involving Magma and the LMFDB.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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