Index Symbol Index C(Γ), 5 C[[q]], 4 Δ, 15 ε(γ), 180 F, 17 f [γ]k , 5 Γ(N), 4 Γ0(N), 5 Γ1(N), 4 Gk(z), 13 GL2(Q), 5 h, 1 h∗, 6 j-function, 170 Mat 2 (Z)n, 131 Mk(G), 123 Mk(G R), 124 Mk(Γ), 7 Mk(N, ε), 128 M k (N, ε), 180 M k , 17 M k , 179 P1(Q), 5 Sk(Γ), 134 Sk, 18 SL2(Z), 1, 5 Algorithm Index p-adic Nullspace, 118 Asymptotically Fast Echelon Form, 111 Baby-step Giant-step Discrete Log, 69 Basis for Mk, 19 Basis of Cusp Forms, 56 Berlekamp-Massey, 116 Bernoulli Number Bn, 32 Conductor, 71 Cremona’s Heilbronn Matrices, 48 Cusp Representation, 135 Decomposition Using Kernels, 119 Dirichlet Character as Kronecker Symbol, 74 Elliptic Curves of Conductor N, 187 Enumerating Eisenstein Series, 88 Evaluate ε, 68 Explicit Cusp Equivalence, 135 Extension of Character, 76 Factorization of Character, 71 Galois Orbit, 76 Gauss Elimination, 104 Generalized Bernoulli Numbers, 84 Hecke Operator, 26 Kronecker Symbol as Dirichlet Character, 74 List P1(Z/NZ), 146 Merel’s Algorithm for Computing a Basis, 165 Minimal Generator for (Z/prZ)∗, 65 Modular Symbols Presentation, 154 Multimodular Echelon Form, 107 Order of Character, 70 Period Integrals, 181 Rational Reconstruction, 106 Reduction in P1(Z/NZ) to Canonical Form, 145 Restriction of Character, 75 Sum over A4(N), 99 System of Eigenvalues, 166 Values of ε, 70 Width of Cusp, 9 265

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