Realization of Modular Galois Representations in Jacobians of modular curves

2019/05/24 by Tian, Peng
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.10036

Abstract

In this paper, we propose an improved algorithm for computing mod ℓ Galois representations associated to eigenforms of arbitrary levels prime to ℓ. Precisely, we present a method to find the Jacobians of modular curves which have the smallest possible dimensions in a well-defined sense to realize the modular Galois representations. This algorithm also works without the assumption ℓ ≥ k-1, where k are the weights of the eigenforms.

Related

• Computing modular Galois representations
• Certification of modular Galois representations
• Computing Galois representations and equations for modular curves X_H(ℓ)
• Computing modular Galois representations for small ℓ
• Moduli-friendly Eisenstein series over the p-adics and the computation of modular Galois representations