/* 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([-28, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([8,8,w + 4]) primes_array = [ [2, 2, -w + 6],\ [2, 2, w + 5],\ [7, 7, 6*w - 35],\ [7, 7, -6*w - 29],\ [9, 3, 3],\ [11, 11, 4*w + 19],\ [11, 11, 4*w - 23],\ [13, 13, -2*w + 11],\ [13, 13, 2*w + 9],\ [25, 5, -5],\ [31, 31, 2*w - 13],\ [31, 31, -2*w - 11],\ [41, 41, -8*w - 39],\ [41, 41, 8*w - 47],\ [53, 53, -26*w - 125],\ [53, 53, 26*w - 151],\ [61, 61, -14*w + 81],\ [61, 61, -14*w - 67],\ [83, 83, 2*w - 15],\ [83, 83, -2*w - 13],\ [97, 97, 2*w - 5],\ [97, 97, -2*w - 3],\ [109, 109, 2*w - 3],\ [109, 109, -2*w - 1],\ [113, 113, 2*w - 1],\ [127, 127, 8*w - 45],\ [127, 127, 8*w + 37],\ [131, 131, -50*w + 291],\ [131, 131, 50*w + 241],\ [139, 139, 6*w - 37],\ [139, 139, -6*w - 31],\ [149, 149, 20*w + 97],\ [149, 149, 20*w - 117],\ [157, 157, -12*w - 59],\ [157, 157, 12*w - 71],\ [163, 163, 4*w - 19],\ [163, 163, 4*w + 15],\ [173, 173, 4*w + 23],\ [173, 173, 4*w - 27],\ [211, 211, 2*w - 19],\ [211, 211, -2*w - 17],\ [227, 227, -4*w - 13],\ [227, 227, 4*w - 17],\ [233, 233, 6*w + 25],\ [233, 233, -6*w + 31],\ [239, 239, -14*w - 69],\ [239, 239, 14*w - 83],\ [241, 241, 46*w + 221],\ [241, 241, -46*w + 267],\ [251, 251, 22*w - 129],\ [251, 251, 22*w + 107],\ [257, 257, -34*w + 197],\ [257, 257, -34*w - 163],\ [277, 277, 4*w - 29],\ [277, 277, -4*w - 25],\ [283, 283, 4*w - 15],\ [283, 283, -4*w - 11],\ [289, 17, -17],\ [307, 307, 68*w - 395],\ [307, 307, 68*w + 327],\ [311, 311, 10*w - 61],\ [311, 311, -10*w - 51],\ [313, 313, -32*w - 155],\ [313, 313, 32*w - 187],\ [317, 317, -18*w - 85],\ [317, 317, 18*w - 103],\ [331, 331, -4*w - 9],\ [331, 331, 4*w - 13],\ [337, 337, -16*w - 79],\ [337, 337, 16*w - 95],\ [347, 347, -12*w + 67],\ [347, 347, 12*w + 55],\ [353, 353, 14*w - 79],\ [353, 353, 14*w + 65],\ [361, 19, -19],\ [367, 367, -32*w - 153],\ [367, 367, -32*w + 185],\ [383, 383, 56*w + 269],\ [383, 383, 56*w - 325],\ [389, 389, -4*w - 27],\ [389, 389, 4*w - 31],\ [401, 401, 8*w - 51],\ [401, 401, -8*w - 43],\ [421, 421, 12*w - 73],\ [421, 421, -12*w - 61],\ [439, 439, -8*w - 33],\ [439, 439, 8*w - 41],\ [443, 443, -4*w - 1],\ [443, 443, 4*w - 5],\ [461, 461, -30*w + 173],\ [461, 461, 30*w + 143],\ [463, 463, 2*w - 25],\ [463, 463, -2*w - 23],\ [467, 467, 34*w + 165],\ [467, 467, 34*w - 199],\ [503, 503, -26*w - 127],\ [503, 503, 26*w - 153],\ [509, 509, 4*w - 33],\ [509, 509, -4*w - 29],\ [521, 521, -10*w + 53],\ [521, 521, 10*w + 43],\ [529, 23, -23],\ [547, 547, 14*w - 85],\ [547, 547, -14*w - 71],\ [557, 557, 66*w + 317],\ [557, 557, 66*w - 383],\ [563, 563, 2*w - 27],\ [563, 563, -2*w - 25],\ [569, 569, -64*w + 373],\ [569, 569, 64*w + 309],\ [587, 587, 12*w + 53],\ [587, 587, -12*w + 65],\ [593, 593, 8*w + 45],\ [593, 593, 8*w - 53],\ [601, 601, -26*w - 123],\ [601, 601, 26*w - 149],\ [617, 617, 6*w - 23],\ [617, 617, -6*w - 17],\ [647, 647, 24*w - 137],\ [647, 647, -24*w - 113],\ [653, 653, 28*w - 165],\ [653, 653, -28*w - 137],\ [677, 677, -22*w - 103],\ [677, 677, 22*w - 125],\ [691, 691, 20*w - 113],\ [691, 691, 20*w + 93],\ [709, 709, -10*w - 41],\ [709, 709, 10*w - 51],\ [719, 719, -8*w + 37],\ [719, 719, -8*w - 29],\ [727, 727, -22*w - 109],\ [727, 727, 22*w - 131],\ [739, 739, 46*w - 269],\ [739, 739, -46*w - 223],\ [761, 761, -6*w - 13],\ [761, 761, 6*w - 19],\ [769, 769, 110*w - 639],\ [769, 769, 110*w + 529],\ [773, 773, 4*w - 37],\ [773, 773, -4*w - 33],\ [787, 787, 2*w - 31],\ [787, 787, -2*w - 29],\ [809, 809, 56*w + 271],\ [809, 809, -56*w + 327],\ [821, 821, 6*w - 17],\ [821, 821, -6*w - 11],\ [823, 823, 38*w - 223],\ [823, 823, -38*w - 185],\ [827, 827, 132*w - 767],\ [827, 827, 132*w + 635],\ [841, 29, -29],\ [853, 853, -76*w + 443],\ [853, 853, 76*w + 367],\ [863, 863, 14*w - 87],\ [863, 863, -14*w - 73],\ [911, 911, 2*w - 33],\ [911, 911, -2*w - 31],\ [919, 919, -6*w - 41],\ [919, 919, 6*w - 47],\ [929, 929, 50*w + 239],\ [929, 929, 50*w - 289],\ [953, 953, 6*w - 11],\ [953, 953, -6*w - 5],\ [967, 967, -8*w - 25],\ [967, 967, 8*w - 33],\ [991, 991, 16*w + 71],\ [991, 991, -16*w + 87]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, 0, -4, -2, 0, 4, 2, -2, 2, -4, 0, 2, -6, -6, 6, -2, 6, 4, 0, 18, -14, 10, -2, 2, -4, -8, -12, 4, 0, 20, 22, -10, -22, -10, -20, -12, -18, -22, 4, 4, -12, 20, -14, -14, -4, 0, -10, -18, -12, -20, 10, -22, -2, -10, -4, -8, 18, -28, 4, -20, 0, -18, -26, 18, 22, 20, 8, 10, -22, -12, 20, 2, 18, 22, -24, 8, -16, 12, 26, -18, 6, -34, -26, -2, 0, 24, 36, -24, -18, 30, 24, -32, 0, 20, 16, 16, 30, 6, 10, -6, -38, 16, 36, -6, 22, -4, -20, -6, 42, 4, -28, 18, 18, 26, 10, -30, 18, -8, 24, -42, 14, 22, 38, 44, 28, -50, -30, 28, -48, -44, -24, -16, 52, 38, -34, 2, -6, 14, -26, -28, 48, 26, -14, -10, 30, -32, -16, 52, 40, -46, -6, 14, -48, 24, 24, -40, 16, 40, 18, 34, 54, 30, 16, 32, -32, -8] 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 + 6])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]