266 Index
Definition Index
Γ-invariant on the left, 206
k-sharblies, 233
q-expansion, 4
Q-rank, 245
abelian variety attached to f, 178
action of Hecke operators, 139
antiholomorphic, 137
arithmetic group, 208
associate proper Q-parabolic subgroups
of G, 212
automorphic form, 209
automorphy factor, 205
Bernoulli numbers, 16
Bianchi groups, 247
Borel conjecture, 212
boundary map, 40, 134
bounded domains, 211
cellular decomposition, 219
character of the modular form, 160
Cholesky decomposition, 214
codimension, 219
complex upper half plane, 1
conductor, 71
congruence subgroup, 4, 208
congruence subgroup problem, 7
Connected, 207
critical integers, 138
cross polytope, 238
cusp form, 4
cuspidal, 209
cuspidal automorphic form, 210
cuspidal cohomology, 212
cuspidal modular symbols, 40, 134
cusps for a congruence subgroup Γ, 5
Defined over Q, 207
degeneracy map, 59, 161
diamond-bracket action, 160
diamond-bracket operators, 128, 159
dimension, 219
Dirichlet character, 64
divisor, xiii
echelon form, 103
eigenforms, 59
Eilenberg–Mac Lane, 211
Eisenstein cohomology, 212
Eisenstein series, 210
Eisenstein subspace, 83
extended modular symbols, 179
extended upper half plane, 6
fan, 218
Farey tessellation, 220
formal power series, 4
Fourier expansion, 3
generalized Bernoulli numbers, 83
generalized modular symbol, 251
Grothendieck motive, 179
group cohomology, 211
Hecke algebra, 54, 83, 128
Hecke correspondence, 225
Hecke operator, 37, 128, 226
Hecke polynomials, 241
height, 107
Hermite normal form, 120, 240
Hermitian symmetric spaces, 211
holomorphic, 2
holomorphic at ∞, 4
holomorphic at the cusp α, 7
Humbert forms, 244
hypersimplices, 246
Krylov methods, 116
Krylov subspace, 116
Laplace–Beltrami–Casimir operator, 209
left action of G, 123
left action of GL2(Q), 40
left action of SL2(Z), 133
left translations, 208
level 1, 4
level of Γ, 4
linear fractional transformations, 1
Maass forms, 210
Manin symbol, 124
meromorphic, 2
meromorphic at ∞, 4
Miller basis, 20
modular complex, 244
modular elliptic curves, 187
modular form, 4, 7
modular function, 4
modular group, 2
modular symbols, 228
modular symbols algorithm, 229
modular symbols for Γ0(N), 40
modular symbols over a ring R, 124
newform, 59, 164
new modular symbols, 143
new subspace, 59, 162
nonnormalized weight k Eisenstein series,
13
normalized Eisenstein series, 17
old modular symbols, 144
old subspace, 161
opposite, 222
perfect, 216
perfection, 244
pivot column, 103
plus one quotient, 165
primitive, 71, 215
primitive character associated to, 71
principal congruence subgroup, 208
Ramanujan function, 25
rational Jordan form, 114
rational period mapping, 185
real-analytic, 210
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