Computational Aspects of Modular Forms and Galois Representations > Chapter 2. Modular curves, modular forms, lattices, Galois representations

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Computational Aspects of Modular Forms and Galois Representations

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Table of Contents

Dependencies between the chapters

Chapter 1. Introduction, main results, context

Chapter 2. Modular curves, modular forms, lattices, Galois representations

2.1 Modular curves

2.2 Modular forms

2.3 Lattices and modular forms

2.4 Galois representations attached to eigenforms

2.5 Galois representations over finite fields, and reduction to torsion in Jacobians

Chapter 3. First description of the algorithms

Chapter 4. Short introduction to heights and Arakelov theory

Chapter 5. Computing complex zeros of polynomials and power series

Chapter 6. Computations with modular forms and Galois representations

Chapter 7. Polynomials for projective representations of level one forms

Chapter 8. Description of X[sub(1)](5l)

Chapter 9. Applying Arakelov theory

Chapter 10. An upper bound for Green functions on Riemann surfaces

Chapter 11. Bounds for Arakelov invariants of modular curves

Chapter 12. Approximating V[sub(f)] over the complex numbers

Chapter 13. Computing V[sub(f)] modulo p

Chapter 14. Computing the residual Galois representations

Chapter 15. Computing coefficients of modular forms

Epilogue

Bibliography

Index

Chapter Two Modular curves, modular forms, lattices, Galois representations by Bas Edixhoven 2.1 MODULAR CURVES As a good reference for getting an overview of the theory of modular curves and modular forms we recommend the article [Di-Im] by Fred Diamond and John Im. This reference is quite complete as results are concerned,

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Chapter 2. Modular curves, modular forms, lattices, Galois representations - Pg. 29