Topics on Modular Galois Representations Modulo Prime Powers

DOI10.1007/978-3-319-70566-8_31zbMath1426.11046arXiv1612.05017OpenAlexW2574786820MaRDI QIDQ4556599

Gabor Wiese, Panagiotis Tsaknias

Publication date: 16 November 2018

Published in: Algorithmic and Experimental Methods in Algebra, Geometry, and Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1612.05017

zbMATH Keywords

databasemodular formsGalois representationslevel loweringlevel raisingmodularity higher congruences

Mathematics Subject Classification ID

Congruences for modular and (p)-adic modular forms (11F33) Galois representations (11F80)

Related Items (1)

Dihedral group, 4-torsion on an elliptic curve, and a peculiar eigenform modulo 4

Uses Software

• Magma
• ArtinAlgebras

Cites Work

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• Structure of Hecke algebras of modular forms modulo \(p\)
• Multiplicities of Galois representations of weight one. With an appendix by Niko Naumann
• Serre's modularity conjecture. I
• The Magma algebra system. I: The user language
• The weight in Serre's conjectures on modular forms
• On modular representations of \(\text{Gal}(\overline{\mathbb Q}/\mathbb Q)\) arising from modular forms
• On the density of modular points in universal deformation spaces
• On certain finiteness questions in the arithmetic of modular forms
• LIFTING TORSION GALOIS REPRESENTATIONS
• A characterization of ordinary modular eigenforms with CM
• Computing Congruences of Modular Forms and Galois Representations Modulo Prime Powers
• The Fontaine-Mazur conjecture for $ {GL}_2$
• Higher congruence companion forms
• The Tamagawa number conjecture of adjoint motives of modular forms
• ON MODULAR GALOIS REPRESENTATIONS MODULO PRIME POWERS

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