Multiplicities of cohomological automorphic forms on GL₂ and mod p representations of GL₂(ℚ_p)

2018/01/30 by Hu, Yongquan
#11F70 #11F75 #22E50 #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1801.10074

Abstract

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 by Marshall. The main tool of the proof is the mod p representation theory of GL₂(ℚ_p) as started by Barthel-Livne and Breuil, and developed by Paskunas.

Related

• Unconditional bounds for the multiplicity of automorphic forms of cohomological type on GL₂
• Multiplicities in the ordinary part of mod p cohomology for GL_n(ℚ_p)
• Bounds for the number of cohomological automorphic representations of GL₃/ℚ in the weight aspect
• Bounds for multiplicities of automorphic forms of cohomological type on GL₂
• Level-raising for automorphic forms on GL_n