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Computational Aspects of Modular Forms and Galois Representations by Robin de Jong, Jean-Marc Couveignes, Franz Merkl, Johan Bosman, Bas Edixhoven

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Chapter Six

Computations with modular forms and Galois representations

by Johan Bosman

In this chapter we will discuss several aspects of the practical side of computating with modular forms and Galois representations. We start by discussing computations with modular forms and from there work toward the computation of polynomials that give the Galois representations associated with modular forms. Throughout this chapter, we will denote the space of cusp forms of weight k, group Γ1(N), and character ε by Sk(N, ε).

6.1 MODULAR SYMBOLS

Modular symbols provide a way of doing symbolic calculations with modular forms, as well as the homology of modular curves. In this section our intention is to give the reader an idea of what is going on rather than ...

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