/* 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([-52, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([4, 2, 2]) primes_array = [ [2, 2, -11*w - 74],\ [2, 2, -11*w + 85],\ [5, 5, 4*w - 31],\ [5, 5, -4*w - 27],\ [9, 3, 3],\ [11, 11, -70*w - 471],\ [13, 13, -2*w - 13],\ [13, 13, -2*w + 15],\ [19, 19, 92*w - 711],\ [23, 23, -26*w + 201],\ [23, 23, -26*w - 175],\ [29, 29, 18*w - 139],\ [29, 29, 18*w + 121],\ [41, 41, -10*w - 67],\ [41, 41, 10*w - 77],\ [47, 47, 2*w - 17],\ [47, 47, 2*w + 15],\ [49, 7, -7],\ [79, 79, 40*w - 309],\ [79, 79, 40*w + 269],\ [107, 107, 4*w + 25],\ [107, 107, -4*w + 29],\ [109, 109, 2*w - 11],\ [109, 109, -2*w - 9],\ [127, 127, 136*w + 915],\ [127, 127, 136*w - 1051],\ [137, 137, -8*w - 55],\ [137, 137, 8*w - 63],\ [151, 151, -16*w - 107],\ [151, 151, 16*w - 123],\ [157, 157, 188*w + 1265],\ [157, 157, 188*w - 1453],\ [163, 163, 14*w + 95],\ [163, 163, 14*w - 109],\ [167, 167, -24*w + 185],\ [167, 167, -24*w - 161],\ [173, 173, 2*w - 7],\ [173, 173, -2*w - 5],\ [191, 191, 2*w - 21],\ [191, 191, -2*w - 19],\ [193, 193, 2*w - 5],\ [193, 193, -2*w - 3],\ [199, 199, 166*w - 1283],\ [199, 199, 166*w + 1117],\ [211, 211, 4*w - 27],\ [211, 211, -4*w - 23],\ [227, 227, 84*w - 649],\ [227, 227, 84*w + 565],\ [229, 229, -100*w + 773],\ [229, 229, -100*w - 673],\ [241, 241, 14*w - 107],\ [241, 241, -14*w - 93],\ [251, 251, -10*w - 69],\ [251, 251, 10*w - 79],\ [281, 281, 6*w + 37],\ [281, 281, -6*w + 43],\ [289, 17, -17],\ [293, 293, 298*w + 2005],\ [293, 293, 298*w - 2303],\ [307, 307, -4*w - 21],\ [307, 307, 4*w - 25],\ [311, 311, 22*w + 149],\ [311, 311, -22*w + 171],\ [313, 313, 16*w - 125],\ [313, 313, -16*w - 109],\ [337, 337, 46*w + 309],\ [337, 337, -46*w + 355],\ [353, 353, -64*w + 495],\ [353, 353, -64*w - 431],\ [367, 367, 2*w - 25],\ [367, 367, -2*w - 23],\ [373, 373, -38*w + 293],\ [373, 373, 38*w + 255],\ [389, 389, 4*w - 37],\ [389, 389, -4*w - 33],\ [397, 397, -12*w - 83],\ [397, 397, 12*w - 95],\ [409, 409, 202*w + 1359],\ [409, 409, 202*w - 1561],\ [419, 419, -50*w + 387],\ [419, 419, 50*w + 337],\ [431, 431, 320*w - 2473],\ [431, 431, 320*w + 2153],\ [439, 439, 128*w - 989],\ [439, 439, 128*w + 861],\ [443, 443, -86*w - 579],\ [443, 443, -86*w + 665],\ [463, 463, 306*w + 2059],\ [463, 463, 306*w - 2365],\ [467, 467, 2*w - 27],\ [467, 467, -2*w - 25],\ [499, 499, 30*w + 203],\ [499, 499, -30*w + 233],\ [523, 523, 68*w + 457],\ [523, 523, 68*w - 525],\ [547, 547, 4*w - 19],\ [547, 547, -4*w - 15],\ [563, 563, -28*w - 187],\ [563, 563, 28*w - 215],\ [569, 569, 150*w - 1159],\ [569, 569, 150*w + 1009],\ [577, 577, 72*w + 485],\ [577, 577, 72*w - 557],\ [587, 587, 262*w - 2025],\ [587, 587, 262*w + 1763],\ [601, 601, -10*w + 73],\ [601, 601, 10*w + 63],\ [607, 607, 16*w - 121],\ [607, 607, -16*w - 105],\ [617, 617, -152*w + 1175],\ [617, 617, -152*w - 1023],\ [619, 619, -6*w - 47],\ [619, 619, 6*w - 53],\ [631, 631, -58*w + 449],\ [631, 631, 58*w + 391],\ [643, 643, -174*w + 1345],\ [643, 643, -174*w - 1171],\ [647, 647, 218*w + 1467],\ [647, 647, 218*w - 1685],\ [653, 653, -196*w - 1319],\ [653, 653, 196*w - 1515],\ [659, 659, -52*w + 401],\ [659, 659, 52*w + 349],\ [673, 673, 482*w + 3243],\ [673, 673, 482*w - 3725],\ [677, 677, 246*w + 1655],\ [677, 677, 246*w - 1901],\ [691, 691, 2*w - 31],\ [691, 691, -2*w - 29],\ [709, 709, 20*w + 137],\ [709, 709, 20*w - 157],\ [719, 719, -94*w + 727],\ [719, 719, -94*w - 633],\ [727, 727, 38*w + 257],\ [727, 727, -38*w + 295],\ [743, 743, -8*w + 55],\ [743, 743, 8*w + 47],\ [757, 757, 12*w - 97],\ [757, 757, 12*w + 85],\ [787, 787, -4*w - 5],\ [787, 787, 4*w - 9],\ [811, 811, 4*w - 7],\ [811, 811, -4*w - 3],\ [823, 823, 6*w - 55],\ [823, 823, -6*w - 49],\ [827, 827, -4*w - 1],\ [827, 827, 4*w - 5],\ [857, 857, 6*w - 35],\ [857, 857, -6*w - 29],\ [859, 859, -10*w - 73],\ [859, 859, 10*w - 83],\ [877, 877, 194*w - 1499],\ [877, 877, 194*w + 1305],\ [881, 881, -8*w - 61],\ [881, 881, 8*w - 69],\ [883, 883, -66*w + 511],\ [883, 883, 66*w + 445],\ [887, 887, 504*w + 3391],\ [887, 887, 504*w - 3895],\ [929, 929, 424*w + 2853],\ [929, 929, 424*w - 3277],\ [941, 941, 386*w - 2983],\ [941, 941, 386*w + 2597],\ [947, 947, 2*w - 35],\ [947, 947, -2*w - 33],\ [953, 953, 22*w - 167],\ [953, 953, -22*w - 145],\ [961, 31, -31]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 1, -2, -2, -3, 2, 3, -3, 0, 5, 5, 3, -3, -12, 12, -8, -8, -5, 12, -12, 3, -3, 3, -3, -12, 12, -19, -19, -18, 18, 0, 0, -6, -6, -12, 12, 18, -18, -11, -11, -6, 6, 7, 7, -3, 3, 3, -3, -12, -12, -24, 24, -20, -20, -12, 12, -33, -9, 9, 12, -12, 11, 11, -21, -21, 18, -18, -31, -31, 8, 8, -21, 21, 26, 26, -2, -2, 6, -6, -14, -14, 24, -24, 0, 0, 22, 22, -32, -32, 8, 8, 18, 18, 9, -9, 36, -36, -24, 24, 24, -24, -15, -15, 28, 28, 6, -6, -12, 12, 10, 10, 24, 24, 0, 0, 32, 32, 23, 23, -10, -10, -15, 15, -48, 48, 3, -3, -8, -8, 8, 8, 43, 43, 35, 35, 6, -6, -12, -12, -9, 9, -33, 33, -3, -3, -15, 15, 24, -24, -54, -54, 27, -27, -34, -34, 24, 24, 24, -24, 41, 41, 27, -27, 46, 46, 30, -30, 26] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, -11*w - 74])] = 1 AL_eigenvalues[ZF.ideal([2, 2, -11*w + 85])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]