Abstract
We present an algorithm for enumerating all odd semisimple two-dimensional mod p Galois representations unramified outside p. We also discuss the implementation of this algorithm in Sage and give a summary of the results we obtained.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Citro, C., Ghitza, A.: Computing level 1 Hecke eigensystems (mod p) (preprint)
Edixhoven, B.: The weight in Serre’s conjectures on modular forms. Invent. Math. 109(3), 563–594 (1992)
Khare, C.: Modularity of Galois representations and motives with good reduction properties. J. Ramanujan Math. Soc. 22(1), 75–100 (2007)
Khare, C., Wintenberger, J.P.: Serre’s modularity conjecture. I. Invent. Math. 178(3), 485–504 (2009), http://dx.doi.org/10.1007/s00222-009-0205-7
Khare, C., Wintenberger, J.P.: Serre’s modularity conjecture. II. Invent. Math. 178(3), 505–586 (2009), http://dx.doi.org/10.1007/s00222-009-0206-6
Lario, J.C., Schoof, R.: Some computations with Hecke rings and deformation rings. Experiment. Math. 11(2), 303–311 (2002), http://projecteuclid.org/getRecord?id=euclid.em/1062621223 ; with an appendix by Amod Agashe and William Stein
Stein, W.: Modular forms, a computational approach. In: Graduate Studies in Mathematics, vol. 79. American Mathematical Society, Providence (2007); With an appendix by Paul E. Gunnells
Stein, W., et al.: Sage Mathematics Software (Version 4.4.1). The Sage Development Team (2010), http://www.sagemath.org
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Citro, C., Ghitza, A. (2010). Enumerating Galois Representations in Sage. In: Fukuda, K., Hoeven, J.v.d., Joswig, M., Takayama, N. (eds) Mathematical Software – ICMS 2010. ICMS 2010. Lecture Notes in Computer Science, vol 6327. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15582-6_44
Download citation
DOI: https://doi.org/10.1007/978-3-642-15582-6_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-15581-9
Online ISBN: 978-3-642-15582-6
eBook Packages: Computer ScienceComputer Science (R0)