CONTENTS ix
25.3. The global unipotent result 293
26. The elliptic terms 294
26.1. Properties of the elliptic orbital integrals 295
26.2. The archimedean elliptic orbital integral 300
26.3. Orders and lattices in an imaginary quadratic field 302
26.4. Local-global theory for lattices 307
26.5. From G(Afin) to lattices in E 310
26.6. The non-archimedean orbital integral for N 1 314
26.7. The case of level N 318
Applications
27. Dimension formulas 333
27.1. The elliptic terms 333
27.2. The unipotent term 337
27.3. The dimension of 5k(7V, a/) and some examples 338
28. Computing Hecke eigenvalues 340
28.1. Obtaining eigenvalues from knowledge of the traces 340
28.2. Integrality of Hecke eigenvalues 343
28.3. The r-function 344
28.4. An example with nontrivial character 347
29. The distribution of Hecke eigenvalues 351
29.1. Bounds for the Eichler-Selberg trace formula 352
29.2. Chebyshev polynomials 355
29.3. Distribution of eigenvalues 356
29.4. Further applications and generalizations 359
30. A recursion relation for traces of Hecke operators 360
Bibliography 363
Tables of notation 368
Statement of the final result 370
Index 373
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