On congruences between normalized eigenforms with different sign at a Steinberg prime
Let f be a newform of weight 2 on Γ0(N) with Fourier q-expansion f(q)=q+∑n≥2anqn, where Γ0(N) denotes the group of invertible matrices with integer coefficients, upper triangular mod N. Let p be a prime dividing N once, p∥N, a Steinberg prime. Then, it is well known that ap∈{1,−1}. We denote by Kf t...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Estado: | Versión aceptada para publicación |
| Fecha de publicación: | 2018 |
| País: | España |
| Institución: | Universidad de Barcelona |
| Repositorio: | Dipòsit Digital de la UB |
| OAI Identifier: | oai:diposit.ub.edu:2445/142921 |
| Acceso en línea: | https://hdl.handle.net/2445/142921 |
| Access Level: | acceso abierto |
| Palabra clave: | Teoria de Galois Formes modulars Galois theory Modular forms |
| Sumario: | Let f be a newform of weight 2 on Γ0(N) with Fourier q-expansion f(q)=q+∑n≥2anqn, where Γ0(N) denotes the group of invertible matrices with integer coefficients, upper triangular mod N. Let p be a prime dividing N once, p∥N, a Steinberg prime. Then, it is well known that ap∈{1,−1}. We denote by Kf the field of coefficients of f. Let λ be a finite place in Kf not dividing 2p and assume that the mod λ Galois representation attached to f is irreducible. In this paper we will give necessary and sufficient conditions for the existence of another Hecke eigenform f′(q)=q+∑n≥2a′nqn p-new of weight 2 on Γ0(N) and a finite place λ′ of Kf′ such that ap=−a′p and the Galois representations ρ¯f,λ and ρ¯f′,λ′ are isomorphic. |
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