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Computational Aspects of Modular Forms and Galois RepresentationsHow One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime (AM-176)$
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Bas Edixhoven and Jean-Marc Couveignes

Print publication date: 2011

Print ISBN-13: 9780691142012

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691142012.001.0001

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Computations with modular forms and Galois representations

Computations with modular forms and Galois representations

Chapter:
(p.129) Chapter Six Computations with modular forms and Galois representations
Source:
Computational Aspects of Modular Forms and Galois Representations
Author(s):

Johan Bosman

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691142012.003.0006

This chapter discusses several aspects of the practical side of computing with modular forms and Galois representations. It starts by discussing computations with modular forms, and from there work towards the computation of polynomials that give the Galois representations associated with modular forms. Throughout, the chapter denotes the space of cusp forms of weight k, group Γ‎₁(N), and character ε‎ by Sₖ(N, ε‎).

Keywords:   modular forms, Galois representations, modular symbols, polynomials, cusp forms

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