/* This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the HMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data. */ P. = PolynomialRing(QQ) g = P([-1, -8, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 9, w - 1]) primes_array = [ [3, 3, -w - 2],\ [5, 5, w + 1],\ [7, 7, w - 3],\ [8, 2, 2],\ [9, 3, w^2 - 3*w - 2],\ [13, 13, w + 3],\ [13, 13, -w + 2],\ [19, 19, -w^2 + 2*w + 4],\ [23, 23, w^2 - 4*w + 1],\ [25, 5, w^2 - 2*w - 1],\ [31, 31, w^2 - 2*w - 9],\ [37, 37, -w^2 + 3*w + 3],\ [41, 41, w^2 - w - 1],\ [41, 41, w^2 - w - 5],\ [41, 41, w^2 - w - 10],\ [43, 43, -2*w - 3],\ [47, 47, -w^2 - w + 4],\ [49, 7, -w^2 + 5*w - 5],\ [59, 59, w^2 - w - 4],\ [59, 59, w^2 - 3],\ [59, 59, w - 5],\ [67, 67, 2*w^2 - 4*w - 9],\ [73, 73, 2*w^2 - 3*w - 12],\ [79, 79, -3*w^2 + 9*w + 5],\ [97, 97, 2*w^2 - w - 14],\ [97, 97, 2*w^2 - 2*w - 13],\ [97, 97, -2*w^2 + 5*w + 5],\ [101, 101, w^2 - w - 11],\ [131, 131, w - 6],\ [139, 139, -2*w^2 + 5*w + 4],\ [149, 149, -3*w + 11],\ [149, 149, -3*w - 4],\ [157, 157, w^2 - 3*w - 6],\ [173, 173, w^2 - 5*w + 3],\ [173, 173, -2*w^2 + 5*w + 8],\ [173, 173, 3*w^2 - 5*w - 17],\ [179, 179, 2*w^2 - w - 11],\ [179, 179, -3*w^2 + 7*w + 12],\ [179, 179, w^2 - 2*w - 12],\ [181, 181, w^2 + w - 16],\ [199, 199, 2*w^2 - 9],\ [211, 211, -w^2 + w - 2],\ [229, 229, -w^2 + 3*w - 3],\ [233, 233, w^2 + w - 7],\ [257, 257, 3*w^2 - 3*w - 20],\ [271, 271, w^2 - 4*w - 13],\ [271, 271, 3*w^2 - 4*w - 19],\ [271, 271, 2*w - 9],\ [277, 277, 3*w^2 - 5*w - 20],\ [281, 281, -w^2 - w + 13],\ [283, 283, -3*w + 8],\ [293, 293, -4*w - 7],\ [307, 307, w^2 + 2*w - 5],\ [311, 311, 2*w^2 - 4*w - 5],\ [313, 313, -w^2 - w - 3],\ [317, 317, -3*w^2 + 8*w + 5],\ [331, 331, -w^2 + 2*w - 3],\ [337, 337, -w - 7],\ [337, 337, w^2 + w - 9],\ [337, 337, 3*w - 5],\ [359, 359, 2*w^2 - 4*w - 15],\ [361, 19, 2*w^2 + w - 5],\ [367, 367, -w^2 - 3],\ [367, 367, 3*w^2 - 11*w + 4],\ [367, 367, -2*w^2 + 9*w - 6],\ [373, 373, 2*w^2 - w - 9],\ [379, 379, 3*w^2 - 5*w - 21],\ [383, 383, w - 8],\ [389, 389, -4*w^2 + 9*w + 15],\ [397, 397, 2*w^2 + w - 4],\ [397, 397, -4*w^2 + 13*w + 5],\ [397, 397, -w^2 - 2*w - 4],\ [401, 401, w^2 - 5*w - 4],\ [421, 421, 3*w^2 - 4*w - 18],\ [431, 431, w^2 - 4*w - 16],\ [433, 433, w^2 - 4*w - 7],\ [439, 439, w^2 + 2*w - 17],\ [457, 457, 2*w^2 - 3],\ [457, 457, 4*w - 3],\ [457, 457, 2*w^2 - 3*w - 6],\ [463, 463, 3*w^2 - 12*w + 7],\ [479, 479, w^2 - 6*w + 6],\ [479, 479, -w^2 + 15],\ [479, 479, -6*w^2 + 19*w + 1],\ [487, 487, 2*w^2 - 7*w - 5],\ [487, 487, w^2 + 5*w + 8],\ [487, 487, 3*w^2 - 6*w - 17],\ [491, 491, -4*w + 15],\ [503, 503, 8*w^2 - 25*w - 5],\ [509, 509, 3*w^2 - 12*w + 4],\ [509, 509, -3*w^2 - 5*w + 6],\ [509, 509, w^2 - w - 14],\ [521, 521, -4*w^2 + 10*w + 11],\ [523, 523, 2*w^2 - 7*w + 4],\ [523, 523, 2*w^2 - 2*w - 7],\ [523, 523, -7*w^2 + 22*w + 8],\ [529, 23, 4*w^2 - 14*w + 3],\ [541, 541, w^2 + 4*w - 3],\ [541, 541, -5*w - 9],\ [541, 541, -5*w^2 + 11*w + 20],\ [557, 557, -w^2 + 5*w - 8],\ [563, 563, 2*w^2 - 15],\ [563, 563, -w^2 - 2*w + 20],\ [563, 563, w^2 - 3*w - 15],\ [569, 569, 2*w^2 - w - 5],\ [577, 577, 2*w^2 - 3*w - 21],\ [587, 587, -4*w^2 + 11*w + 6],\ [599, 599, 2*w^2 + 2*w - 9],\ [607, 607, -3*w - 10],\ [613, 613, 4*w^2 - 7*w - 25],\ [631, 631, -3*w^2 + 7*w + 7],\ [641, 641, 3*w^2 - 2*w - 17],\ [641, 641, -3*w^2 + 14*w - 12],\ [641, 641, -5*w^2 + 15*w + 9],\ [643, 643, -5*w - 8],\ [647, 647, 3*w^2 - w - 21],\ [653, 653, w^2 + 7*w + 9],\ [673, 673, -3*w^2 - 2*w + 9],\ [683, 683, 5*w^2 - 17*w + 2],\ [683, 683, 3*w^2 - 6*w - 11],\ [683, 683, 2*w^2 - 7*w - 6],\ [691, 691, w^2 + 3*w + 6],\ [701, 701, 2*w^2 - 5*w - 19],\ [709, 709, -3*w^2 + 9*w + 8],\ [727, 727, 3*w - 13],\ [739, 739, -w - 9],\ [743, 743, 5*w - 3],\ [743, 743, 2*w^2 - 5*w - 13],\ [743, 743, 3*w^2 - 3*w - 17],\ [757, 757, 3*w^2 - 4*w - 16],\ [761, 761, w^2 + 4*w - 4],\ [769, 769, 3*w^2 - w - 15],\ [773, 773, -w^2 + 2*w - 5],\ [787, 787, -2*w^2 + 10*w - 9],\ [797, 797, w^2 - 4*w - 17],\ [811, 811, 6*w^2 - 20*w + 1],\ [811, 811, -w^2 + 4*w - 7],\ [811, 811, 4*w - 9],\ [821, 821, 2*w^2 - 5*w - 14],\ [823, 823, -5*w^2 + 14*w + 8],\ [827, 827, 3*w^2 - w - 22],\ [829, 829, -3*w^2 + 6*w + 10],\ [859, 859, -9*w^2 + 29*w + 2],\ [859, 859, 4*w^2 - 13*w + 2],\ [859, 859, -w^2 + w - 5],\ [863, 863, 2*w^2 + w - 13],\ [877, 877, w^2 + 2*w - 11],\ [881, 881, 2*w^2 - 8*w + 7],\ [883, 883, 3*w^2 + 3*w - 4],\ [907, 907, w^2 + 2*w - 13],\ [929, 929, -3*w - 11],\ [937, 937, w^2 - 5*w - 12],\ [941, 941, 5*w - 4],\ [947, 947, 4*w^2 - 7*w - 20],\ [953, 953, 2*w^2 + 6*w - 3],\ [961, 31, 5*w^2 - 8*w - 29],\ [967, 967, -5*w^2 + 14*w + 7],\ [971, 971, w^2 - 5*w - 10],\ [977, 977, 2*w^2 - 4*w - 23],\ [977, 977, w^2 - 8*w + 17],\ [977, 977, 3*w^2 - 19],\ [991, 991, 3*w^2 - 4*w - 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 1, 2, 5, -2, 5, -3, -6, 0, 3, -6, -7, 6, 3, 11, -6, 6, -1, 14, 0, 6, 10, 11, 8, -18, -13, -5, 17, 6, 16, -6, 22, 21, 5, 9, 18, -20, -10, -10, 1, -20, 22, -27, -5, 14, -28, -14, 16, -26, -9, -26, 17, -30, -6, -1, 9, -26, 3, 2, -9, -6, 23, 24, -12, -12, -26, 16, 6, 9, -2, 25, 5, -17, -35, 38, 7, 26, -6, 35, 7, -24, -32, -18, 10, 34, -30, 18, 12, 32, -15, -15, 1, 39, -12, -26, 32, -1, -19, -11, 2, -35, 36, -8, 20, 22, 27, -14, 24, -28, -3, 16, 27, -9, -2, -14, -20, -39, -1, -14, -28, 16, 10, -35, -10, 0, 34, 10, -36, -34, 22, -34, 7, -42, 32, 1, 2, 32, -8, -18, 34, 18, -47, -14, 4, -20, -38, -7, -33, 44, 26, 22, -29, 1, 26, 23, 35, -14, -48, 55, 54, 47, -32] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, -w - 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]