On \(\mathrm{PGL}_2(\mathbb{F}_7)\) and \(\mathrm{PSL}_2(\mathbb{F}_7)\) number fields ramified at a single prime

DOI10.1016/j.jnt.2024.08.006MaRDI QIDQ6633566

Takeshi Ogasawara, George J. Schaeffer

Publication date: 6 November 2024

Published in: Journal of Number Theory (Search for Journal in Brave)

zbMATH Keywords

Galois representationsramification\(\bmod p\) modular forms of weight one\(\mathrm{PGL}_2(\mathbb{F}_7)\) polynomial\(\mathrm{PSl}_2(\mathbb{F}_7)\) polynomial

Mathematics Subject Classification ID

Galois theory (11R32) Congruences for modular and (p)-adic modular forms (11F33) Holomorphic modular forms of integral weight (11F11) Algebraic number theory computations (11Y40) Galois representations (11F80)

Cites Work

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• On Galois representations of weight one
• Hecke stability and weight 1 modular forms
• Companion forms and explicit computation of \(\mathrm{PGL}_2\) number fields with very little ramification
• Non-minimal modularity lifting in weight one
• Even icosahedral Galois representations of prime conductor
• Dihedral universal deformations
• A database of number fields
• Computational Aspects of Modular Forms and Galois Representations
• Induction formula for the Artin conductors of mod ℓ Galois representations
• Advanced Topics in Computional Number Theory
• Inverse Galois Theory
• Number Fields Ramified at One Prime
• Computing Weight One Modular Forms over $\mathbb{C}$ and $\overline{\mathbb{F}}_{p}$
• Multi-parameter polynomials with given Galois group

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