Index 267
reduced, 234
reducing point, 230
regular, 219
relative to the cusps, 39
restriction of scalars, 207
right action of SL2(Z), 44, 125
right translation, 209
satisfies condition Cn, 131
self-adjoint homogeneous cone, 248
Semisimple, 207
set of cusps, 5
Set of real points, 207
sharbly complex, 233
sigma function, 15
slowly increasing, 209
split form of SLn, 207
split symplectic group, 208
standard fundamental domain, 17
star involution, 141
strong deformation retract, 219
symplectic sharbly complex, 250
tilings, 245
topological cell, 218
transportable, 182
unimodular, 229
virtual cohomological dimension, 215
Voronoˇ ı decomposition, 219
Voronoˇ ı polyhedron, 215
Voronoˇ ı reduction algorithm, 218
weakly modular function, 3, 5
Weierstrass ℘-function, 14
weight, 3, 4, 7
weight k modular symbols for G, 123
weight k right action, 5
well-rounded retract, 219
width of the cusp, 6, 8
SAGE Index
SAGE , ix, xii, 2, 15, 16, 20, 22, 26, 30,
41, 43, 45, 51, 52, 56, 58, 63, 65–67,
74, 77, 78, 85, 89, 95, 106, 144, 161,
163, 198
M36, 28
q-expansion of Δ, 15
SL2(Z), 2
Z/NZ, 65
basis for M24, 20
basis for S2(Γ0(N)), 56
Bernoulli numbers, 16
Bernoulli numbers modulo p, 30
boundary map, 52
continued fraction convergents, 43
cuspidal submodule, 52
dimension formulas, 93
dimension Sk(Γ0(N)), 95
dimension Sk(Γ1(N)), 97
dimension with character, 101, 161
Dirichlet character tutorial, 78
Dirichlet group, 67
echelon form, 112
Eisenstein arithmetic, 26
Eisenstein series, 89
evaluation of character, 67
generalized Bernoulli numbers, 85
Hecke operators M2(Γ0(39)), 50
Hecke operators M2(Γ0(6)), 49
Hecke operator T2, 49
Heilbronn matrices, 49
Manin symbols, 45
Miller basis, 22
modular symbols, 44
modular symbols of level 11, 41
modular symbols printing, 46
rational reconstruction, 106
General Index
Basmaji’s trick, 133
Bernoulli numbers
generalized, 83
Birch and Swinnerton-Dyer conjecture,
10
boundary map, 134
computing, 51
boundary modular symbols
and Manin symbols, 134
congruent number problem, 10
conjecture
Maeda, 28
Shimura-Taniyama, 37
cusp forms
Δ, 14
for Γ, 134
higher level dimension, 92, 96
cuspidal modular symbols
and Manin symbols, 134
cusps
action of SL2(Z) on, 5
and boundary map, 134
criterion for vanishing, 136
dimension
cusp forms of higher level, 92, 96
Diophantine equations, 10
Dirichlet character, 142
and cusps, 136
Eisenstein series, 13
algorithm to enumerate, 88
and Bernoulli numbers, 83
are eigenforms, 88
basis of, 88
compute, 63
compute using SAGE, 89
Fourier expansion, 15
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