/* 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([-98, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([6,6,5*w - 52]) primes_array = [ [2, 2, -17*w - 160],\ [2, 2, -17*w + 177],\ [3, 3, -842*w + 8767],\ [7, 7, -2*w + 21],\ [7, 7, 2*w + 19],\ [13, 13, -12*w - 113],\ [13, 13, 12*w - 125],\ [17, 17, 182*w - 1895],\ [17, 17, 182*w + 1713],\ [23, 23, -512*w - 4819],\ [23, 23, 512*w - 5331],\ [25, 5, -5],\ [29, 29, 22*w - 229],\ [29, 29, 22*w + 207],\ [43, 43, 114*w + 1073],\ [43, 43, 114*w - 1187],\ [47, 47, 8*w - 83],\ [47, 47, -8*w - 75],\ [61, 61, -1172*w - 11031],\ [61, 61, 1172*w - 12203],\ [71, 71, 216*w + 2033],\ [71, 71, 216*w - 2249],\ [83, 83, 8932*w - 93001],\ [83, 83, -2196*w + 22865],\ [109, 109, -4*w - 39],\ [109, 109, 4*w - 43],\ [121, 11, -11],\ [131, 131, 5564*w - 57933],\ [137, 137, 2*w - 17],\ [137, 137, -2*w - 15],\ [149, 149, 18*w - 187],\ [149, 149, 18*w + 169],\ [151, 151, -1502*w - 14137],\ [151, 151, -1502*w + 15639],\ [173, 173, -6*w - 55],\ [173, 173, 6*w - 61],\ [193, 193, 808*w - 8413],\ [193, 193, -808*w - 7605],\ [197, 197, 2*w - 15],\ [197, 197, -2*w - 13],\ [211, 211, -70*w + 729],\ [211, 211, -70*w - 659],\ [227, 227, 284*w + 2673],\ [227, 227, 284*w - 2957],\ [251, 251, 124*w - 1291],\ [251, 251, 124*w + 1167],\ [257, 257, 42*w + 395],\ [257, 257, 42*w - 437],\ [271, 271, 410*w + 3859],\ [271, 271, 410*w - 4269],\ [277, 277, 4*w - 45],\ [277, 277, -4*w - 41],\ [281, 281, -3550*w - 33413],\ [281, 281, 3550*w - 36963],\ [283, 283, 2*w - 27],\ [283, 283, -2*w - 25],\ [293, 293, 2*w - 11],\ [293, 293, -2*w - 9],\ [307, 307, -6*w - 59],\ [307, 307, 6*w - 65],\ [337, 337, 376*w - 3915],\ [337, 337, 376*w + 3539],\ [347, 347, -4*w - 33],\ [347, 347, -4*w + 37],\ [359, 359, -8*w - 73],\ [359, 359, -8*w + 81],\ [361, 19, -19],\ [367, 367, -774*w + 8059],\ [367, 367, -774*w - 7285],\ [379, 379, -30*w + 313],\ [379, 379, -30*w - 283],\ [389, 389, 2*w - 3],\ [389, 389, -2*w - 1],\ [397, 397, -172*w + 1791],\ [397, 397, -172*w - 1619],\ [401, 401, 6*w - 59],\ [401, 401, 6*w + 53],\ [409, 409, -40*w - 377],\ [409, 409, 40*w - 417],\ [419, 419, 100*w - 1041],\ [419, 419, -100*w - 941],\ [421, 421, 308*w + 2899],\ [421, 421, 308*w - 3207],\ [439, 439, 274*w - 2853],\ [439, 439, 274*w + 2579],\ [443, 443, -52*w - 489],\ [443, 443, 52*w - 541],\ [449, 449, 15338*w - 159701],\ [449, 449, -6918*w + 72031],\ [457, 457, 17352*w - 180671],\ [457, 457, 6224*w - 64805],\ [461, 461, 614*w - 6393],\ [461, 461, 614*w + 5779],\ [479, 479, 192*w - 1999],\ [479, 479, 192*w + 1807],\ [487, 487, -94*w + 979],\ [487, 487, -94*w - 885],\ [491, 491, -20*w - 187],\ [491, 491, 20*w - 207],\ [503, 503, -16*w + 165],\ [503, 503, 16*w + 149],\ [509, 509, 2890*w - 30091],\ [509, 509, -2890*w - 27201],\ [521, 521, 11970*w - 124633],\ [521, 521, -10286*w + 107099],\ [577, 577, -1104*w - 10391],\ [577, 577, 1104*w - 11495],\ [593, 593, 134*w + 1261],\ [593, 593, 134*w - 1395],\ [601, 601, -8*w - 79],\ [601, 601, 8*w - 87],\ [613, 613, -2492*w - 23455],\ [613, 613, 2492*w - 25947],\ [617, 617, 226*w - 2353],\ [617, 617, 226*w + 2127],\ [631, 631, 2*w - 33],\ [631, 631, -2*w - 31],\ [677, 677, -62*w - 583],\ [677, 677, 62*w - 645],\ [691, 691, 1798*w - 18721],\ [691, 691, -1798*w - 16923],\ [739, 739, 74*w + 697],\ [739, 739, 74*w - 771],\ [743, 743, 48*w - 499],\ [743, 743, 48*w + 451],\ [757, 757, -44*w + 459],\ [757, 757, -44*w - 415],\ [761, 761, 14*w + 129],\ [761, 761, 14*w - 143],\ [769, 769, 16*w + 153],\ [769, 769, 16*w - 169],\ [773, 773, 4574*w - 47625],\ [773, 773, -39938*w + 415839],\ [787, 787, 3846*w + 36199],\ [787, 787, 3846*w - 40045],\ [809, 809, 30*w + 281],\ [809, 809, -30*w + 311],\ [811, 811, 1070*w - 11141],\ [811, 811, -1070*w - 10071],\ [829, 829, -4*w - 47],\ [829, 829, 4*w - 51],\ [857, 857, -18*w + 185],\ [857, 857, 18*w + 167],\ [877, 877, -196*w - 1845],\ [877, 877, -196*w + 2041],\ [881, 881, -26*w - 243],\ [881, 881, 26*w - 269],\ [907, 907, -14*w - 135],\ [907, 907, -14*w + 149],\ [937, 937, 8*w - 89],\ [937, 937, -8*w - 81],\ [941, 941, 294*w - 3061],\ [941, 941, 294*w + 2767],\ [947, 947, 4*w - 27],\ [947, 947, -4*w - 23],\ [961, 31, -31],\ [971, 971, -1604*w + 16701],\ [971, 971, 1604*w + 15097],\ [983, 983, 144*w - 1499],\ [983, 983, 144*w + 1355],\ [991, 991, -10*w - 99],\ [991, 991, 10*w - 109],\ [997, 997, 604*w - 6289],\ [997, 997, 604*w + 5685]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^3 - x^2 - 2*x + 1 K. = NumberField(heckePol) hecke_eigenvalues_array = [-1, e, -1, e - 2, 1, e^2 - 2*e + 1, 2*e^2 - 1, 3*e^2 - e - 2, 2*e^2 + 2*e - 7, e^2 + e + 3, -e^2 - 4*e + 6, 2*e^2 - 2, 5*e^2 - 5*e - 7, 2*e^2 - 2, -2*e^2 + 2*e + 6, 6*e^2 - 5*e - 6, e^2 - 5*e + 3, -3*e^2 + 9*e + 3, 3*e^2 + 4*e - 10, 8*e^2 - 6*e - 12, 2*e^2 + 5*e - 10, -2*e^2 + e + 5, 9*e^2 - 4*e - 6, -2*e^2 - 4*e + 6, -9*e^2 + 10*e + 13, 5*e^2 - 5*e - 16, -2*e^2 + e + 9, 3*e^2 - 13*e - 1, -10*e^2 + 10*e + 13, 7*e^2 - 6*e + 2, -5*e^2 + e + 18, 3*e^2 - 3*e - 7, 7*e^2 - 7*e - 10, -e^2 - 9*e + 3, -4*e^2 - 9*e + 17, -10*e^2 - e + 22, -7*e^2 - 8*e + 15, e^2 - 11*e + 4, 16*e^2 - 13*e - 23, -8*e^2 + e + 26, -6*e^2 + 4*e + 8, 5*e^2 - 5*e - 12, 3*e^2 - 8*e - 14, -14*e^2 + 5*e + 18, -3*e^2 + 3*e - 15, -6*e^2 + 6*e + 17, e^2 - 2*e + 21, -20*e^2 + 9*e + 25, 9*e^2 - 2*e - 18, -2*e^2 + 3*e + 1, -7*e^2 - 6*e + 4, -7*e^2 + 19*e + 20, 3*e^2 - 2*e + 3, 11*e^2 - 8*e + 5, 12*e^2 - 2*e - 28, -5*e^2 + 6*e + 23, 6*e^2 - 10*e - 13, 16*e^2 - 17*e - 26, -2*e^2 - 9*e + 20, -3*e^2 - 8*e, 5*e^2 + 9*e - 13, 16*e^2 - 11*e - 26, 9*e - 16, 21*e^2 - 4*e - 32, 24*e^2 - 15*e - 32, 4*e^2 + 8*e - 4, -13*e^2 - 3*e + 20, -4*e^2 + 17*e - 2, -26*e^2 + 9*e + 38, 7*e^2 - 23*e - 11, -e^2 + 3*e - 17, -6*e^2 + 5*e + 8, -16*e^2 + 4*e + 20, 7*e^2 - 4*e - 32, -3*e^2 + 3*e - 15, 8*e^2 - 21*e - 9, -12*e^2 - e + 7, -22*e^2 + 5*e + 36, -15*e^2 + 11*e + 20, -9*e^2 - 3*e + 28, 10*e^2 - 8*e - 30, -2*e^2 + e + 4, 3*e^2 + 16*e - 8, 14*e^2 - e - 28, -12*e^2 + 11*e + 27, -15*e^2 + 24*e + 20, -3*e^2 + 5*e + 29, -22*e^2 + 14*e + 20, 6*e^2 + 12*e - 19, -8*e^2 - 3*e + 20, 7*e^2 - 19*e - 28, 7*e^2 - 7*e - 14, 3*e^2 + 10*e + 6, 20*e^2 - 6*e - 37, 18*e^2 - 16*e - 31, 10*e^2 - 16*e - 8, 15*e^2 - 3*e - 27, 4*e^2 - 2*e - 4, -3*e^2 + 24*e - 6, 24*e^2 - 15*e - 37, -6*e^2 + 27*e + 8, 13*e^2 - 11*e - 22, 20*e^2 - 15*e - 28, -7*e - 16, -25*e^2 + 12*e + 31, 5*e^2 - 5*e - 15, -30*e^2 + 17*e + 39, -20*e^2 + 24*e + 22, -7*e^2 - 2*e + 25, 8*e^2 + 5*e - 10, -2*e^2 - 4*e - 23, -17*e^2 + 15*e + 23, -2*e^2 - 11*e + 18, 18*e^2 + 4*e - 20, -16*e^2 + 15*e + 23, 7*e^2 - 18*e, -2*e^2 + 16*e - 8, -e^2 + 42, -15*e^2 - 10*e + 41, -5*e^2 - 5*e - 15, -21*e^2 + 20*e + 41, 14*e^2 + 11*e - 40, -22*e^2 + 3*e + 48, -10*e^2 - 4*e + 16, -e^2 - 12*e + 1, -13*e^2 + 3*e - 3, -12*e^2 + 17*e + 24, 14*e^2 + e - 25, -21*e^2 + 28*e + 40, -4*e^2 + 20*e + 7, -34*e^2 + 25*e + 41, -3*e^2 - 6*e + 7, -6*e^2 + 3*e + 44, 7*e^2 - 10*e + 16, -11*e^2 + 31*e + 16, -20*e^2 + 14*e + 9, -18*e^2 + 15*e + 38, -20*e^2 + 23*e + 10, 13*e^2 + 20*e - 44, 20*e^2 - 22*e - 19, -26*e^2 + 26*e + 30, 17*e^2 - 26*e - 22, -16*e^2 - 4*e + 25, -11*e^2 + 9*e + 32, -e^2 + 8*e - 16, -24*e + 18, -11*e^2 + 21*e - 1, -5*e^2 + 16*e + 18, 2*e^2 - 21*e - 25, -18*e^2 + 5*e + 11, -e^2 + 55, -7*e^2 + 3*e, -9*e^2 - 17*e + 17, -e^2 + 22*e + 13, -4*e^2 + 17*e - 7, -2*e^2 - 40, 22*e^2 - 17*e - 25, 6*e^2 - 7*e + 40, 14*e^2 - 3*e + 11, 25*e^2 - 23*e - 24, 15*e^2 + 8*e - 12, -13*e^2 - 2*e + 62, 26*e^2 + 7*e - 39, -12*e^2 + 30*e + 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([2,2,17*w + 160])] = 1 AL_eigenvalues[ZF.ideal([3,3,842*w + 7925])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]