/* 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([-26, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([15, 15, w + 7]) primes_array = [ [2, 2, w],\ [2, 2, w + 1],\ [3, 3, w + 1],\ [5, 5, 2*w - 11],\ [7, 7, w + 3],\ [13, 13, w],\ [13, 13, w + 12],\ [23, 23, w + 8],\ [23, 23, w + 14],\ [41, 41, 2*w - 9],\ [41, 41, -2*w - 7],\ [53, 53, w + 11],\ [53, 53, w + 41],\ [59, 59, 4*w + 17],\ [59, 59, 4*w - 21],\ [73, 73, w + 27],\ [73, 73, w + 45],\ [79, 79, -6*w - 29],\ [79, 79, 6*w - 35],\ [89, 89, 2*w - 5],\ [89, 89, -2*w - 3],\ [97, 97, w + 34],\ [97, 97, w + 62],\ [101, 101, 2*w - 3],\ [101, 101, -2*w - 1],\ [103, 103, w + 32],\ [103, 103, w + 70],\ [107, 107, w + 15],\ [107, 107, w + 91],\ [109, 109, 4*w - 25],\ [109, 109, -4*w - 21],\ [113, 113, w + 30],\ [113, 113, w + 82],\ [121, 11, -11],\ [131, 131, 4*w - 19],\ [131, 131, -4*w - 15],\ [137, 137, w + 33],\ [137, 137, w + 103],\ [151, 151, 2*w - 17],\ [151, 151, -2*w - 15],\ [157, 157, w + 66],\ [157, 157, w + 90],\ [197, 197, w + 20],\ [197, 197, w + 176],\ [211, 211, 6*w - 37],\ [211, 211, 6*w + 31],\ [223, 223, w + 47],\ [223, 223, w + 175],\ [233, 233, w + 86],\ [233, 233, w + 146],\ [251, 251, 4*w - 15],\ [251, 251, -4*w - 11],\ [263, 263, w + 23],\ [263, 263, w + 239],\ [269, 269, 6*w - 29],\ [269, 269, 6*w + 23],\ [283, 283, w + 58],\ [283, 283, w + 224],\ [289, 17, -17],\ [307, 307, w + 121],\ [307, 307, w + 185],\ [311, 311, 8*w + 33],\ [311, 311, 8*w - 41],\ [313, 313, w + 61],\ [313, 313, w + 251],\ [317, 317, w + 115],\ [317, 317, w + 201],\ [331, 331, -14*w - 67],\ [331, 331, 14*w - 81],\ [347, 347, w + 105],\ [347, 347, w + 241],\ [361, 19, -19],\ [367, 367, w + 101],\ [367, 367, w + 265],\ [379, 379, 2*w - 23],\ [379, 379, -2*w - 21],\ [397, 397, w + 180],\ [397, 397, w + 216],\ [419, 419, 4*w - 3],\ [419, 419, 4*w - 1],\ [421, 421, -4*w - 27],\ [421, 421, 4*w - 31],\ [433, 433, w + 188],\ [433, 433, w + 244],\ [443, 443, w + 136],\ [443, 443, w + 306],\ [461, 461, -6*w - 19],\ [461, 461, 6*w - 25],\ [479, 479, -24*w + 133],\ [479, 479, -16*w + 87],\ [499, 499, -6*w - 35],\ [499, 499, 6*w - 41],\ [509, 509, 10*w + 41],\ [509, 509, 10*w - 51],\ [521, 521, -30*w + 167],\ [521, 521, -14*w + 75],\ [523, 523, w + 72],\ [523, 523, w + 450],\ [541, 541, 4*w - 33],\ [541, 541, -4*w - 29],\ [557, 557, w + 208],\ [557, 557, w + 348],\ [571, 571, 2*w - 27],\ [571, 571, -2*w - 25],\ [577, 577, w + 166],\ [577, 577, w + 410],\ [607, 607, w + 85],\ [607, 607, w + 521],\ [617, 617, w + 35],\ [617, 617, w + 581],\ [631, 631, 34*w - 193],\ [631, 631, 14*w - 83],\ [643, 643, w + 275],\ [643, 643, w + 367],\ [653, 653, w + 36],\ [653, 653, w + 616],\ [683, 683, w + 202],\ [683, 683, w + 480],\ [709, 709, 12*w - 73],\ [709, 709, 12*w + 61],\ [719, 719, -8*w - 27],\ [719, 719, 8*w - 35],\ [727, 727, w + 194],\ [727, 727, w + 532],\ [733, 733, w + 342],\ [733, 733, w + 390],\ [739, 739, -10*w - 53],\ [739, 739, 10*w - 63],\ [743, 743, w + 261],\ [743, 743, w + 481],\ [751, 751, 26*w - 149],\ [751, 751, 22*w - 127],\ [761, 761, -18*w + 97],\ [761, 761, -34*w + 189],\ [787, 787, w + 177],\ [787, 787, w + 609],\ [827, 827, w + 81],\ [827, 827, w + 745],\ [839, 839, -8*w - 25],\ [839, 839, 8*w - 33],\ [841, 29, -29],\ [853, 853, w + 92],\ [853, 853, w + 760],\ [863, 863, w + 259],\ [863, 863, w + 603],\ [881, 881, 6*w - 11],\ [881, 881, -6*w - 5],\ [919, 919, 2*w - 33],\ [919, 919, -2*w - 31],\ [929, 929, -6*w - 1],\ [929, 929, 6*w - 7],\ [937, 937, w + 441],\ [937, 937, w + 495],\ [941, 941, 6*w - 5],\ [941, 941, 6*w - 1],\ [947, 947, w + 199],\ [947, 947, w + 747],\ [953, 953, w + 416],\ [953, 953, w + 536],\ [961, 31, -31],\ [971, 971, 12*w - 59],\ [971, 971, 12*w + 47],\ [977, 977, w + 44],\ [977, 977, w + 932],\ [991, 991, -6*w - 41],\ [991, 991, 6*w - 47],\ [997, 997, w + 109],\ [997, 997, w + 887]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 1, 1, 1, 0, 2, 2, 0, 0, 10, 10, 10, 10, -4, -4, -10, -10, 0, 0, -6, -6, -2, -2, 6, 6, 16, 16, 12, 12, 14, 14, -2, -2, -6, -12, -12, 6, 6, -8, -8, -14, -14, -6, -6, 20, 20, -8, -8, 6, 6, 12, 12, -16, -16, 14, 14, 12, 12, -30, -28, -28, -24, -24, -26, -26, 2, 2, 12, 12, 28, 28, -22, 24, 24, -20, -20, 2, 2, 4, 4, -26, -26, 14, 14, 12, 12, -18, -18, 0, 0, 4, 4, -34, -34, 10, 10, -4, -4, 30, 30, 18, 18, -4, -4, -2, -2, 8, 8, 6, 6, -8, -8, 36, 36, -46, -46, -36, -36, -26, -26, -48, -48, 16, 16, -14, -14, -44, -44, 16, 16, 16, 16, -6, -6, -28, -28, 28, 28, 40, 40, -54, -6, -6, 56, 56, -46, -46, 40, 40, 34, 34, 54, 54, -50, -50, 36, 36, 22, 22, -62, 60, 60, -2, -2, 32, 32, -54, -54] 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 + 1])] = -1 AL_eigenvalues[ZF.ideal([5, 5, 2*w - 11])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]