INDEX algebra anisotropic automorphic form binary form canonical automorphism canonical involution capacity ideal Center of a Clifford algebra claSS of a lattice class of a symmetric matrix ClaSS n u m b e r of an algebraic group class number of an order Clifford algebra Clifford group Conductor of an order congruence subgroup 165, core dimension core subspace cusp form 170,, denominator ideal discriminant algebra discriminant field discriminan t of a quadratic form discriminan t of an order 13 9 169,230 120 16 16 75,210 19 81 91 81 116 16 20 106 205,229 11 11 206,230 44 12 12 12 106 eigenfunction of differential operators 247 elementary divisor even Clifford algebra even Clifford group exceptional prime genUS of a lattice genUS of a symmetric matrix geilUS of maximal lattices global field Hasse principle Hecke algebra Hecke character Hecke eigenform 170, involution isotropic Laplace-Beltrami operator lattice local field 44 17 20 83 81 91 83 37 60 73 ix 207,232 13 9 144,158 37 37 main involution mass maximal lattice maximal order Order in an algebra origin orthogonal basis orthogonal complement orthogonal group parabolic subgroup (£, L)-primitive positive involution primitive matrix primitive solutions proper ideal quaternion algebra reduced expression reduced norm reduced trace simple algebra special orthogonal group spherical function spin group spin representation spinor norm split Witt decomposition strong approximation sum of 3 squares sum of 5, 7, 9 squares symmetry totally isotropic two-sided ideal weak approximation weak Witt decomposition Witt decomposition Witt's theorem 15 133 45 37 37 149,156 12 9 9 29 95 262 44 1 107 14 44 14 14 13 9 246 23 268 24 11 81 118,119 123,135 21 9 37 85 11 11 10 275

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