Multiplicities of cohomological automorphic forms on GL(2) and mod p representations of GL2(Q(p))(Yongquan Hu)----Academy of Mathematics and Systems Science

We prove a new upper bound for the dimension of the space of cohomological automorphic forms of fixed level and growing parallel weight on GL2 over a number field which is not totally real, improving the one obtained in [Ann. of Math. (2) 175 (2012)]. The main tool of the proof is the mod p representation theory of GL2(Qp) as started by Barthel–Livné and Breuil, and developed by Pa？kunas.

Publication:

- Journal of the European Mathematical Society, 23, 11, 3625-3678 (2021),

Authors:

- Yongquan Hu (Morningside Center of Mathematics, AMSS, Chinese Academy of Sciences)