Contents ix
§8.1. Modular Symbols 122
§8.2. Manin Symbols 124
§8.3. Hecke Operators 128
§8.4. Cuspidal Modular Symbols 133
§8.5. Pairing Modular Symbols and Modular Forms 137
§8.6. Degeneracy Maps 142
§8.7. Explicitly Computing Mk(Γ0(N)) 144
§8.8. Explicit Examples 147
§8.9. Refined Algorithm for the Presentation 154
§8.10. Applications 155
§8.11. Exercises 156
Chapter 9. Computing with Newforms 159
§9.1. Dirichlet Character Decomposition 159
§9.2. Atkin-Lehner-Li Theory 161
§9.3. Computing Cusp Forms 165
§9.4. Congruences between Newforms 170
§9.5. Exercises 176
Chapter 10. Computing Periods 177
§10.1. The Period Map 178
§10.2. Abelian Varieties Attached to Newforms 178
§10.3. Extended Modular Symbols 179
§10.4. Approximating Period Integrals 180
§10.5. Speeding Convergence Using Atkin-Lehner 183
§10.6. Computing the Period Mapping 185
§10.7. All Elliptic Curves of Given Conductor 187
§10.8. Exercises 190
Chapter 11. Solutions to Selected Exercises 191
§11.1. Chapter 1 191
§11.2. Chapter 2 193
§11.3. Chapter 3 194
§11.4. Chapter 4 196
§11.5. Chapter 5 197
§11.6. Chapter 6 197
§11.7. Chapter 7 198
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