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

Mat2(Z)n, 131

Mk(G), 123

Mk(G; R), 124

Mk(Γ), 7

Mk(N, ε), 128

Mk(N, ε), 180

Mk, 17

Mk, 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