On Galois Representations of Weight One

TL;DR

This paper constructs a two-dimensional Galois representation associated with Katz modular forms of weight one over finite fields and demonstrates its unramified nature at prime p in most cases.

Contribution

It introduces a novel Galois representation linked to weight one Katz modular forms and analyzes its ramification properties at p.

Findings

Representation is unramified at p in most cases

Establishes a connection between Galois representations and weight one modular forms

Provides new insights into the structure of Galois representations in characteristic p

Abstract

A two-dimensional Galois representation into the Hecke algebra of Katz modular forms of weight one over a finite field of characteristic p is constructed and is shown to be unramified at p in most cases.