Computations of Galois representations associated to modular forms of level one

Peng Tian. "Computations of Galois representations associated to modular forms of level one." Acta Arithmetica 164.4 (2014): 399-411. <http://eudml.org/doc/279674>.

@article{PengTian2014,
abstract = { We propose an improved algorithm for computing mod ℓ Galois representations associated to a cusp form f of level one. The proposed method allows us to explicitly compute the case with ℓ = 29 and f of weight k = 16, and the cases with ℓ = 31 and f of weight k = 12,20,22. All the results are rigorously proved to be correct. As an example, we will compute the values modulo 31 of Ramanujan's tau function at some huge primes up to a sign. Also we will give an improved uper bound on Lehmer's conjecture for Ramanujan's tau function. },
author = {Peng Tian},
journal = {Acta Arithmetica},
keywords = {modular Galois representations; modular forms; modular curves; polynomials; Ramanujan's tau function},
language = {eng},
number = {4},
pages = {399-411},
title = {Computations of Galois representations associated to modular forms of level one},
url = {http://eudml.org/doc/279674},
volume = {164},
year = {2014},
}

TY - JOUR
AU - Peng Tian
TI - Computations of Galois representations associated to modular forms of level one
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 4
SP - 399
EP - 411
AB - We propose an improved algorithm for computing mod ℓ Galois representations associated to a cusp form f of level one. The proposed method allows us to explicitly compute the case with ℓ = 29 and f of weight k = 16, and the cases with ℓ = 31 and f of weight k = 12,20,22. All the results are rigorously proved to be correct. As an example, we will compute the values modulo 31 of Ramanujan's tau function at some huge primes up to a sign. Also we will give an improved uper bound on Lehmer's conjecture for Ramanujan's tau function.
LA - eng
KW - modular Galois representations; modular forms; modular curves; polynomials; Ramanujan's tau function
UR - http://eudml.org/doc/279674
ER -