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
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