268 Index

Eisenstein subspace, 83

Fermat’s last theorem, 10

Hecke algebra

generators over Z, 175

Hecke operator, 54, 225

Heilbronn matrices, 48, 132, 133, 148,

150

SAGE, 49

Krylov subspace, 114

lattices, 11

linear symmetric spaces, 245

Maeda’s conjecture, 28

Manin symbols, 44

and boundary space, 134

and cuspidal subspace, 134

modular symbols

finite presentation, 44

new and old subspace of, 143

newform, 155

associated period map, 177

computing, 159

system of eigenvalues, 166

new modular symbols, 143

number field sieve, 69

old modular symbols, 143

partitions, 11

period mapping

computation of, 185

Petersson inner product, 59, 160

Ramanujan graphs, 10

right action of GL2(Q),

5

Serre’s conjecture, 11

Shimura-Taniyama conjecture, 37

valence formula, 17