Certification of modular Galois representations
Copyright policy )Certification of modular Galois representations
We show how the output of the algorithm to compute modular Galois representations previously described by the author [Rend. Circ. Mat. Palermo (2) 62 (2013), no. 3, 451–476] can be certified. We have used this process to compute certified tables of such Galois representations obtained thanks to an improved version of this algorithm, including representations modulo primes up to 31 31 and representations attached to a newform with nonrational (but of course algebraic) coefficients, which had never been done before. These computations take place in the Jacobian of modular curves of genus up to 26 26 .
Effective Galois theory, Certification, Mathematics - Number Theory, Galois representations, Galois theory, Algebraic number theory computations, Computational methods (permutation groups), 11Y70, 11F11, 11F80, 11S20, 11Y40, 20B40, 20J06, FOS: Mathematics, Number Theory (math.NT), Cohomology of groups, QA, Holomorphic modular forms of integral weight, Group cohomology, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
Effective Galois theory, Certification, Mathematics - Number Theory, Galois representations, Galois theory, Algebraic number theory computations, Computational methods (permutation groups), 11Y70, 11F11, 11F80, 11S20, 11Y40, 20B40, 20J06, FOS: Mathematics, Number Theory (math.NT), Cohomology of groups, QA, Holomorphic modular forms of integral weight, Group cohomology, [MATH.MATH-NT] Mathematics [math]/Number Theory [math.NT]
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