/* 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([-54, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([28, 14, 996*w - 7834]) primes_array = [ [2, 2, -w + 8],\ [2, 2, w + 7],\ [3, 3, -52*w - 357],\ [3, 3, -52*w + 409],\ [7, 7, 498*w - 3917],\ [13, 13, 22*w - 173],\ [13, 13, 22*w + 151],\ [17, 17, -6*w - 41],\ [17, 17, -6*w + 47],\ [25, 5, -5],\ [31, 31, 1048*w - 8243],\ [61, 61, 602*w - 4735],\ [61, 61, 602*w + 4133],\ [67, 67, -186*w - 1277],\ [67, 67, -186*w + 1463],\ [71, 71, 290*w - 2281],\ [71, 71, 290*w + 1991],\ [73, 73, 2*w - 13],\ [73, 73, -2*w - 11],\ [83, 83, -36*w - 247],\ [83, 83, 36*w - 283],\ [89, 89, -126*w - 865],\ [89, 89, 126*w - 991],\ [107, 107, 2*w - 19],\ [107, 107, -2*w - 17],\ [109, 109, -12*w - 83],\ [109, 109, 12*w - 95],\ [113, 113, -112*w - 769],\ [113, 113, 112*w - 881],\ [121, 11, -11],\ [139, 139, 4*w + 25],\ [139, 139, -4*w + 29],\ [149, 149, 68*w - 535],\ [149, 149, -68*w - 467],\ [163, 163, 6*w - 49],\ [163, 163, -6*w - 43],\ [167, 167, 1152*w - 9061],\ [167, 167, 1152*w + 7909],\ [181, 181, 2*w - 7],\ [181, 181, -2*w - 5],\ [191, 191, 26*w + 179],\ [191, 191, 26*w - 205],\ [193, 193, -216*w + 1699],\ [193, 193, -216*w - 1483],\ [199, 199, -16*w - 109],\ [199, 199, 16*w - 125],\ [211, 211, 54*w - 425],\ [211, 211, 54*w + 371],\ [223, 223, -8*w + 61],\ [223, 223, 8*w + 53],\ [229, 229, 14*w - 109],\ [229, 229, -14*w - 95],\ [233, 233, 736*w + 5053],\ [233, 233, 736*w - 5789],\ [241, 241, 10*w + 67],\ [241, 241, -10*w + 77],\ [251, 251, 2148*w + 14747],\ [251, 251, 2148*w - 16895],\ [269, 269, 810*w - 6371],\ [269, 269, 810*w + 5561],\ [271, 271, -200*w - 1373],\ [271, 271, 200*w - 1573],\ [281, 281, -424*w + 3335],\ [281, 281, -424*w - 2911],\ [313, 313, 334*w + 2293],\ [313, 313, 334*w - 2627],\ [317, 317, 28*w - 221],\ [317, 317, -28*w - 193],\ [353, 353, 6*w + 37],\ [353, 353, -6*w + 43],\ [359, 359, 2*w - 25],\ [359, 359, -2*w - 23],\ [361, 19, -19],\ [367, 367, 64*w + 439],\ [367, 367, 64*w - 503],\ [373, 373, -84*w - 577],\ [373, 373, -84*w + 661],\ [379, 379, -18*w - 125],\ [379, 379, 18*w - 143],\ [383, 383, 48*w - 377],\ [383, 383, 48*w + 329],\ [409, 409, 914*w - 7189],\ [409, 409, 914*w + 6275],\ [421, 421, -1836*w - 12605],\ [421, 421, -1836*w + 14441],\ [431, 431, 70*w - 551],\ [431, 431, 70*w + 481],\ [433, 433, 2698*w + 18523],\ [433, 433, 2698*w - 21221],\ [443, 443, 2386*w - 18767],\ [443, 443, -2386*w - 16381],\ [461, 461, 438*w + 3007],\ [461, 461, 438*w - 3445],\ [509, 509, 6*w - 41],\ [509, 509, -6*w - 35],\ [523, 523, 2252*w - 17713],\ [523, 523, 2252*w + 15461],\ [529, 23, -23],\ [541, 541, -276*w - 1895],\ [541, 541, 276*w - 2171],\ [547, 547, -6*w - 47],\ [547, 547, 6*w - 53],\ [587, 587, -12*w + 91],\ [587, 587, 12*w + 79],\ [599, 599, 158*w - 1243],\ [599, 599, -158*w - 1085],\ [601, 601, 62*w - 487],\ [601, 601, 62*w + 425],\ [617, 617, -32*w - 221],\ [617, 617, 32*w - 253],\ [619, 619, 244*w - 1919],\ [619, 619, -244*w - 1675],\ [643, 643, -4*w - 13],\ [643, 643, 4*w - 17],\ [647, 647, 408*w + 2801],\ [647, 647, 408*w - 3209],\ [653, 653, 4*w - 41],\ [653, 653, -4*w - 37],\ [659, 659, -10*w - 73],\ [659, 659, 10*w - 83],\ [677, 677, 18*w + 121],\ [677, 677, 18*w - 139],\ [683, 683, 2*w - 31],\ [683, 683, -2*w - 29],\ [701, 701, -380*w + 2989],\ [701, 701, -380*w - 2609],\ [719, 719, 1464*w + 10051],\ [719, 719, 1464*w - 11515],\ [751, 751, 6*w - 55],\ [751, 751, -6*w - 49],\ [761, 761, 1122*w - 8825],\ [761, 761, 1122*w + 7703],\ [773, 773, 2802*w - 22039],\ [773, 773, 2802*w + 19237],\ [787, 787, 4*w - 11],\ [787, 787, -4*w - 7],\ [797, 797, -6*w - 31],\ [797, 797, 6*w - 37],\ [829, 829, 646*w + 4435],\ [829, 829, 646*w - 5081],\ [841, 29, -29],\ [859, 859, -4*w - 1],\ [859, 859, 4*w - 5],\ [877, 877, 1524*w + 10463],\ [877, 877, 1524*w - 11987],\ [881, 881, 138*w + 947],\ [881, 881, -138*w + 1085],\ [907, 907, 2178*w - 17131],\ [907, 907, -2178*w - 14953],\ [919, 919, 18*w - 145],\ [919, 919, -18*w - 127],\ [929, 929, 6*w - 35],\ [929, 929, -6*w - 29],\ [941, 941, -3798*w - 26075],\ [941, 941, 3798*w - 29873],\ [977, 977, -7024*w + 55247],\ [977, 977, -4928*w + 38761],\ [983, 983, 168*w + 1153],\ [983, 983, -168*w + 1321]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -1, -2, -2, 1, -4, -4, 6, 6, -10, -4, 8, 8, -4, -4, 0, 0, 2, 2, -6, -6, -6, -6, 12, 12, 2, 2, 6, 6, -22, 14, 14, -18, -18, -16, -16, -12, -12, 20, 20, 24, 24, 14, 14, 20, 20, -4, -4, 8, 8, -4, -4, -6, -6, -10, -10, -18, -18, -12, -12, -16, -16, -6, -6, -10, -10, 6, 6, 18, 18, -24, -24, -34, 8, 8, 14, 14, -16, -16, 36, 36, 14, 14, -10, -10, 24, 24, -34, -34, -12, -12, 12, 12, 36, 36, 2, 2, -46, 38, 38, 8, 8, -42, -42, -24, -24, 26, 26, 6, 6, 26, 26, 14, 14, -12, -12, 18, 18, -24, -24, -12, -12, -12, -12, 18, 18, 12, 12, -40, -40, -18, -18, 24, 24, -22, -22, -12, -12, 56, 56, -22, 14, 14, -22, -22, -54, -54, 44, 44, 56, 56, 6, 6, -24, -24, -6, -6, -36, -36] 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 + 8])] = 1 AL_eigenvalues[ZF.ideal([2, 2, w + 7])] = 1 AL_eigenvalues[ZF.ideal([7, 7, 498*w - 3917])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]