/* 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([-32, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([8,4,2*w + 10]) primes_array = [ [2, 2, -w + 6],\ [2, 2, -w - 5],\ [3, 3, -28*w - 145],\ [5, 5, -6*w - 31],\ [5, 5, -6*w + 37],\ [13, 13, -4*w - 21],\ [13, 13, 4*w - 25],\ [29, 29, -2*w + 11],\ [29, 29, -2*w - 9],\ [31, 31, 50*w + 259],\ [31, 31, 50*w - 309],\ [43, 43, -106*w - 549],\ [49, 7, -7],\ [67, 67, 2*w - 15],\ [67, 67, -2*w - 13],\ [71, 71, -40*w + 247],\ [71, 71, 40*w + 207],\ [79, 79, 14*w - 87],\ [79, 79, 14*w + 73],\ [89, 89, 10*w + 51],\ [89, 89, 10*w - 61],\ [97, 97, -72*w - 373],\ [97, 97, 72*w - 445],\ [103, 103, -26*w - 135],\ [103, 103, 26*w - 161],\ [109, 109, -4*w - 23],\ [109, 109, -4*w + 27],\ [113, 113, 2*w - 5],\ [113, 113, -2*w - 3],\ [121, 11, -11],\ [127, 127, 2*w - 17],\ [127, 127, -2*w - 15],\ [131, 131, 20*w + 103],\ [131, 131, 20*w - 123],\ [137, 137, 6*w - 35],\ [137, 137, 6*w + 29],\ [139, 139, 10*w + 53],\ [139, 139, 10*w - 63],\ [149, 149, -118*w - 611],\ [149, 149, -118*w + 729],\ [179, 179, 52*w - 321],\ [179, 179, 52*w + 269],\ [181, 181, 60*w - 371],\ [181, 181, -60*w - 311],\ [191, 191, -96*w - 497],\ [191, 191, 96*w - 593],\ [193, 193, 24*w - 149],\ [193, 193, 24*w + 125],\ [227, 227, 4*w - 19],\ [227, 227, -4*w - 15],\ [229, 229, -36*w - 187],\ [229, 229, 36*w - 223],\ [233, 233, -22*w + 135],\ [233, 233, -22*w - 113],\ [257, 257, 174*w + 901],\ [257, 257, 386*w + 1999],\ [263, 263, 32*w + 165],\ [263, 263, 32*w - 197],\ [271, 271, 2*w - 21],\ [271, 271, -2*w - 19],\ [283, 283, -6*w - 35],\ [283, 283, -6*w + 41],\ [289, 17, -17],\ [307, 307, 82*w - 507],\ [307, 307, 82*w + 425],\ [337, 337, -8*w - 45],\ [337, 337, -8*w + 53],\ [347, 347, 4*w - 15],\ [347, 347, -4*w - 11],\ [361, 19, -19],\ [367, 367, 18*w + 95],\ [367, 367, 18*w - 113],\ [379, 379, 70*w - 433],\ [379, 379, -70*w - 363],\ [383, 383, 8*w - 45],\ [383, 383, 8*w + 37],\ [389, 389, 230*w + 1191],\ [389, 389, 442*w + 2289],\ [397, 397, -12*w + 77],\ [397, 397, -12*w - 65],\ [419, 419, 12*w - 71],\ [419, 419, 12*w + 59],\ [439, 439, -6*w + 43],\ [439, 439, -6*w - 37],\ [449, 449, 18*w + 91],\ [449, 449, 18*w - 109],\ [467, 467, -4*w - 5],\ [467, 467, 4*w - 9],\ [487, 487, -138*w - 715],\ [487, 487, 138*w - 853],\ [491, 491, 4*w - 7],\ [491, 491, -4*w - 3],\ [503, 503, 208*w + 1077],\ [503, 503, -208*w + 1285],\ [521, 521, 10*w + 47],\ [521, 521, 10*w - 57],\ [529, 23, -23],\ [541, 541, 228*w - 1409],\ [541, 541, -228*w - 1181],\ [547, 547, 2*w - 27],\ [547, 547, -2*w - 25],\ [587, 587, -36*w + 221],\ [587, 587, -36*w - 185],\ [593, 593, 98*w - 605],\ [593, 593, 98*w + 507],\ [613, 613, 564*w + 2921],\ [613, 613, -284*w - 1471],\ [619, 619, -10*w + 67],\ [619, 619, -10*w - 57],\ [641, 641, 46*w - 283],\ [641, 641, 46*w + 237],\ [643, 643, 866*w + 4485],\ [643, 643, 194*w + 1005],\ [647, 647, 56*w + 289],\ [647, 647, 56*w - 345],\ [653, 653, 142*w - 877],\ [653, 653, 142*w + 735],\ [661, 661, -340*w - 1761],\ [661, 661, 508*w + 2631],\ [677, 677, -6*w - 19],\ [677, 677, 6*w - 25],\ [709, 709, 4*w - 37],\ [709, 709, -4*w - 33],\ [743, 743, 88*w - 543],\ [743, 743, -88*w - 455],\ [761, 761, 6*w - 23],\ [761, 761, -6*w - 17],\ [769, 769, -16*w + 103],\ [769, 769, -16*w - 87],\ [773, 773, 38*w - 233],\ [773, 773, 38*w + 195],\ [787, 787, -18*w - 97],\ [787, 787, 18*w - 115],\ [823, 823, 54*w - 335],\ [823, 823, -54*w - 281],\ [839, 839, 8*w - 39],\ [839, 839, -8*w - 31],\ [853, 853, -4*w - 35],\ [853, 853, 4*w - 39],\ [863, 863, 48*w + 247],\ [863, 863, 48*w - 295],\ [877, 877, 148*w - 915],\ [877, 877, -148*w - 767],\ [883, 883, -306*w - 1585],\ [883, 883, 306*w - 1891],\ [887, 887, 24*w + 121],\ [887, 887, 24*w - 145],\ [907, 907, -182*w - 943],\ [907, 907, 182*w - 1125],\ [911, 911, 320*w + 1657],\ [911, 911, 744*w + 3853],\ [919, 919, -90*w - 467],\ [919, 919, 90*w - 557],\ [929, 929, 398*w + 2061],\ [929, 929, 610*w + 3159],\ [953, 953, -198*w - 1025],\ [953, 953, 198*w - 1223],\ [967, 967, 698*w + 3615],\ [967, 967, -362*w - 1875],\ [983, 983, 32*w + 163],\ [983, 983, 32*w - 195]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 0, -1, 0, 3, 2, -1, -6, 9, 8, 8, 8, -4, -4, -10, 9, -6, -10, -1, 15, 3, -16, 8, 2, -1, 2, 2, 21, -3, -7, -19, 8, 6, 6, 18, 12, -4, -10, 15, 12, -18, -18, -7, 20, 15, -6, 14, -16, -18, -12, -25, 20, -3, 18, 6, -30, -30, -9, -4, -16, 5, -13, -31, -16, 29, 8, 2, -12, -27, -25, 26, 17, 5, -1, -9, 0, -24, -9, -16, -7, -3, -12, 5, -22, 30, -6, -12, 18, -7, 38, 12, -24, -12, 39, 12, -12, 14, 14, 2, -19, -4, 39, -36, 30, 21, 2, -34, -28, 35, 24, -30, -40, 14, 0, 6, 15, 42, -10, 32, -18, 42, -28, 41, 3, 6, -33, 21, -22, -22, 30, 27, -13, -49, 14, -37, 51, -36, 5, -16, -24, -45, -7, -22, -7, 44, 3, 36, -46, -16, -15, -54, 11, -52, -12, -18, -42, 6, 50, -1, -21, -30] 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,w + 5])] = -1 AL_eigenvalues[ZF.ideal([2,2,w - 6])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]