A level raising result for modular Galois representations modulo prime powers

2012/03/29 by Tsaknias, Panagiotis
#11F33 #11F80 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1203.6541

Abstract

In this work we provide a level raising theorem for \mod λⁿ modular Galois representations. It allows one to see such a Galois representation that is modular of level N, weight 2 and trivial Nebentypus as one that is modular of level Np, for a prime p coprime to N, when a certain local condition at p is satisfied. It is a generalization of a result of Ribet concerning \mod ℓ Galois representations.

Related

• Topics on modular Galois representations modulo prime powers
• On modular Galois representations modulo prime powers
• On the computation of Galois representations associated to level one modular forms
• Non-optimal levels of a reducible mod l modular representation
• Modularity of certain mod pⁿ Galois representations