Computations of Galois representations associated to modular forms of level one

DOI10.4064/aa164-4-5zbMath1334.11092arXiv1311.0577OpenAlexW3104307292MaRDI QIDQ2875430

Peng Tian

Publication date: 14 August 2014

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1311.0577

zbMATH Keywords

polynomialsmodular curvesmodular formsmodular Galois representationsRamanujan's tau function

Mathematics Subject Classification ID

Modular and automorphic functions (11F03) Galois representations (11F80) Software, source code, etc. for problems pertaining to number theory (11-04) Analytic computations (11Y35)

Related Items (4)

Computing Fourier Coefficients of Level One Modular Forms ⋮ Realization of modular Galois representations in the Jacobians of modular curves ⋮ Moduli-friendly Eisenstein series over the \(p\)-adics and the computation of modular Galois representations ⋮ Non-vanishing Fourier coefficients of \(\Delta_k\)

Uses Software

• Magma
• SageMath

Cites Work

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• Computing modular Galois representations
• Serre's modularity conjecture. II
• On the modular representations of degree two of \(\text{Gal}({\overline {\mathbb Q}}/{\mathbb Q})\)
• The Magma algebra system. I: The user language
• The weight in Serre's conjectures on modular forms
• Approximating rings of integers in number fields
• The vanishing of Ramanujan's function \(\tau(n)\)
• Elliptic Curves Over Finite Fields and the Computation of Square Roots mod p
• Galois group computation for rational polynomials

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