Multiplicities of Galois representations of weight one (with an appendix by Niko Naumann)

TL;DR

This paper investigates mod p Galois representations of weight one, showing that those unramified at p with scalar Frobenius have multiplicities greater than one, revealing new insights into their structure.

Contribution

It proves that the multiplicity of certain mod p Galois representations of weight one, unramified at p with scalar Frobenius, exceeds one, a novel result in the field.

Findings

Multiplicities of specific Galois representations are greater than one.

Scalar Frobenius at p influences the multiplicity of representations.

Provides new understanding of the structure of weight one Galois representations.

Abstract

In this article we consider mod p modular Galois representations which are unramified at p such that the Frobenius element at p acts through a scalar matrix. The principal result states that the multiplicity of any such representation is bigger than 1.