Chapters in this book

1. Frontmatter i
2. Contents v
3. Preface ix
4. Acknowledgments x
5. Author information xi
6. Dependencies between the chapters xii
7. Chapter 1. Introduction, main results, context 1
8. Chapter 2. Modular curves, modular forms, lattices, Galois representations 29
9. Chapter 3. First description of the algorithms 69
10. Chapter 4. Short introduction to heights and Arakelov theory 79
11. Chapter 5. Computing complex zeros of polynomials and power series 95
12. Chapter 6. Computations with modular forms and Galois representations 129
13. Chapter 7. Polynomials for projective representations of level one forms 159
14. Chapter 8. Description of X1(5l) 173
15. Chapter 9. Applying Arakelov theory 187
16. Chapter 10. An upper bound for Green functions on Riemann surfaces 203
17. Chapter 11. Bounds for Arakelov invariants of modular curves 217
18. Chapter 12. Approximating Vf over the complex numbers 257
19. Chapter 13. Computing Vf modulo p 337
20. Chapter 14. Computing the residual Galois representations 371
21. Chapter 15. Computing coefficients of modular forms 383
22. Epilogue 399
23. Bibliography 403
24. Index 423