/* 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([-6, -9, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, w^2 - 3*w - 3]) primes_array = [ [2, 2, -w^2 + 2*w + 2],\ [2, 2, w + 1],\ [3, 3, w^2 - w - 9],\ [7, 7, w^2 - w - 7],\ [11, 11, w^2 - w - 1],\ [13, 13, -2*w - 1],\ [17, 17, -2*w^2 + 6*w + 5],\ [31, 31, -2*w^2 + 2*w + 19],\ [37, 37, 2*w^2 - 13],\ [41, 41, w^2 - w - 5],\ [43, 43, 2*w^2 - 2*w - 17],\ [43, 43, -2*w + 7],\ [43, 43, 12*w^2 - 8*w - 101],\ [49, 7, w^2 + w - 1],\ [59, 59, -w^2 + w + 11],\ [61, 61, -w^2 - w - 1],\ [79, 79, -2*w^2 + 4*w + 7],\ [83, 83, 2*w - 1],\ [89, 89, 5*w^2 - 3*w - 43],\ [103, 103, -2*w + 5],\ [107, 107, -w^2 - 3*w + 1],\ [109, 109, w^2 - 3*w + 1],\ [113, 113, -2*w^2 + 8*w + 7],\ [121, 11, -7*w^2 + 5*w + 61],\ [125, 5, -5],\ [127, 127, 18*w^2 - 12*w - 151],\ [131, 131, w^2 + w - 13],\ [137, 137, 4*w^2 - 4*w - 31],\ [139, 139, -2*w - 7],\ [139, 139, 4*w^2 - 2*w - 31],\ [139, 139, -19*w^2 + 13*w + 161],\ [149, 149, w^2 + w - 7],\ [149, 149, w^2 - 7*w - 5],\ [149, 149, 6*w^2 - 4*w - 53],\ [151, 151, w^2 - 5*w - 5],\ [157, 157, 20*w^2 - 14*w - 169],\ [169, 13, 4*w^2 - 2*w - 35],\ [179, 179, w^2 - 3*w - 13],\ [181, 181, 4*w^2 - 12*w - 11],\ [193, 193, -3*w^2 + 7*w + 11],\ [193, 193, 2*w^2 - 4*w - 23],\ [193, 193, -w^2 + w - 1],\ [197, 197, 3*w^2 - 3*w - 29],\ [197, 197, -2*w^2 + 6*w + 7],\ [197, 197, w^2 - 3*w - 7],\ [199, 199, 26*w^2 - 18*w - 221],\ [211, 211, -4*w - 5],\ [211, 211, 9*w^2 - 7*w - 77],\ [211, 211, 3*w^2 - 7*w - 5],\ [223, 223, 11*w^2 - 7*w - 91],\ [227, 227, 3*w^2 - w - 25],\ [229, 229, 2*w^2 - 4*w - 11],\ [233, 233, 2*w^2 + 6*w + 5],\ [241, 241, w^2 - w - 13],\ [241, 241, w^2 + w - 11],\ [241, 241, 4*w + 1],\ [251, 251, 2*w^2 - 11],\ [257, 257, 4*w^2 - 8*w - 7],\ [263, 263, 5*w^2 - 5*w - 47],\ [263, 263, 5*w^2 - 11*w - 11],\ [263, 263, 2*w^2 - 2*w - 11],\ [269, 269, 6*w^2 - 6*w - 55],\ [269, 269, 8*w^2 - 18*w - 17],\ [269, 269, -2*w^2 + 19],\ [271, 271, 2*w^2 - 17],\ [277, 277, 2*w^2 + 2*w - 1],\ [281, 281, 4*w + 7],\ [289, 17, 10*w^2 - 6*w - 83],\ [317, 317, 2*w^2 + 10*w + 7],\ [317, 317, 22*w^2 - 16*w - 187],\ [317, 317, 4*w^2 - 10*w - 7],\ [347, 347, 2*w^2 - 2*w - 1],\ [349, 349, 4*w^2 - 16*w - 13],\ [353, 353, 2*w^2 - 2*w - 5],\ [367, 367, 23*w^2 - 17*w - 197],\ [373, 373, w^2 - 5*w - 1],\ [397, 397, -6*w^2 + 12*w + 11],\ [401, 401, 2*w^2 + 2*w - 5],\ [419, 419, -3*w^2 - 5*w - 1],\ [421, 421, 14*w^2 - 10*w - 121],\ [439, 439, 3*w^2 - w - 31],\ [443, 443, 2*w^2 - 4*w - 13],\ [449, 449, 29*w^2 - 21*w - 247],\ [457, 457, 2*w^2 - 4*w - 25],\ [457, 457, 9*w^2 - 7*w - 73],\ [457, 457, 7*w^2 - 13*w - 13],\ [461, 461, 6*w^2 - 14*w - 17],\ [461, 461, 2*w^2 - 8*w - 5],\ [461, 461, 15*w^2 - 11*w - 125],\ [463, 463, -3*w^2 + 5*w + 7],\ [467, 467, 3*w^2 + 3*w - 11],\ [479, 479, -w^2 + 5*w - 1],\ [479, 479, 5*w^2 - w - 37],\ [479, 479, 2*w^2 - 4*w - 1],\ [487, 487, 3*w^2 - 3*w - 19],\ [491, 491, 5*w^2 - w - 35],\ [521, 521, -w^2 - 9*w - 7],\ [541, 541, 2*w^2 - 6*w + 1],\ [557, 557, 47*w^2 - 33*w - 401],\ [557, 557, 2*w^2 - 5],\ [557, 557, -13*w^2 + 9*w + 113],\ [563, 563, 10*w^2 - 8*w - 85],\ [569, 569, 4*w^2 - 2*w - 29],\ [587, 587, -3*w^2 + 7*w + 13],\ [593, 593, w^2 - 3*w - 17],\ [607, 607, 8*w^2 - 4*w - 65],\ [613, 613, 6*w^2 - 6*w - 47],\ [617, 617, -8*w - 7],\ [619, 619, 5*w^2 - 5*w - 41],\ [619, 619, 3*w^2 - w - 19],\ [619, 619, 36*w^2 - 26*w - 305],\ [631, 631, w^2 + 3*w - 5],\ [641, 641, -w^2 - w + 17],\ [653, 653, 5*w^2 - 5*w - 43],\ [653, 653, -3*w^2 - 7*w - 5],\ [653, 653, -4*w^2 + 8*w + 19],\ [659, 659, 3*w^2 - 5*w - 11],\ [661, 661, -5*w^2 + 11*w + 13],\ [683, 683, 5*w^2 - 3*w - 47],\ [701, 701, 11*w^2 - 9*w - 91],\ [701, 701, 6*w + 17],\ [701, 701, 7*w^2 - 21*w - 19],\ [709, 709, w^2 - 7*w + 11],\ [719, 719, -23*w^2 + 15*w + 193],\ [719, 719, -5*w^2 + 9*w + 23],\ [719, 719, 10*w^2 - 6*w - 85],\ [727, 727, -6*w^2 + 4*w + 55],\ [733, 733, -4*w^2 + 8*w + 13],\ [739, 739, 3*w^2 - 3*w - 31],\ [739, 739, 16*w^2 - 12*w - 139],\ [739, 739, 9*w^2 - 9*w - 67],\ [751, 751, 2*w^2 - 4*w - 17],\ [757, 757, 3*w^2 + 3*w - 1],\ [761, 761, -3*w^2 + 5*w + 31],\ [809, 809, 3*w^2 - 3*w - 17],\ [823, 823, -6*w^2 + 16*w + 17],\ [827, 827, -9*w^2 + 27*w + 23],\ [829, 829, -3*w^2 + 9*w + 11],\ [853, 853, 6*w^2 - 2*w - 47],\ [857, 857, 10*w^2 - 8*w - 89],\ [877, 877, -3*w^2 - w + 37],\ [881, 881, -w^2 + 3*w - 5],\ [883, 883, -w^2 - 3*w - 7],\ [883, 883, -2*w^2 - 6*w - 7],\ [883, 883, 4*w^2 - 29],\ [887, 887, -4*w^2 + 14*w + 13],\ [887, 887, 8*w^2 - 8*w - 73],\ [887, 887, 2*w - 11],\ [919, 919, -6*w^2 + 6*w + 53],\ [929, 929, -7*w^2 + 19*w + 19],\ [937, 937, 7*w^2 - 15*w - 25],\ [937, 937, 2*w^2 - 25],\ [937, 937, 2*w^2 - 6*w - 11],\ [947, 947, 8*w^2 - 8*w - 59],\ [953, 953, w^2 + 3*w - 7],\ [961, 31, 6*w^2 - 14*w - 11],\ [967, 967, 7*w^2 - 5*w - 55],\ [971, 971, 42*w^2 - 30*w - 359],\ [977, 977, 2*w^2 + 4*w - 7],\ [983, 983, 2*w^2 - 8*w + 1],\ [983, 983, 2*w^2 + 2*w - 13],\ [983, 983, -2*w - 11],\ [991, 991, 6*w^2 - 6*w - 43],\ [997, 997, w^2 - 5*w - 11]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 0, 0, 5, 0, 2, 0, -7, -1, 0, -13, -13, -13, 11, 0, -1, -4, 0, 0, -13, 0, 17, 0, -22, 0, -19, 0, 0, -7, -7, -7, 0, 0, 0, -19, 11, -22, 0, -19, 23, 23, 23, 0, 0, 0, -28, -16, -16, -16, 5, 0, 29, 0, -31, -31, -31, 0, 0, 0, 0, 0, 0, 0, 0, 29, 5, 0, -34, 0, 0, 0, 0, 23, 0, 35, 38, 35, 0, 0, 41, -28, 0, 0, -31, -31, -31, 0, 0, 0, 20, 0, 0, 0, 0, 44, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 29, 47, 0, 17, 17, 17, -1, 0, 0, 0, 0, 0, -49, 0, 0, 0, 0, -22, 0, 0, 0, 44, -7, 53, 53, 53, 11, 29, 0, 0, -52, 0, -46, 35, 0, -25, 0, 8, 8, 8, 0, 0, 0, -52, 0, 35, 35, 35, 0, 0, -13, 41, 0, 0, 0, 0, 0, -61, -10] 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 - w - 9])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]