/* 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([-8, -14, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([8, 4, -w]) primes_array = [ [2, 2, -1/2*w^2 + 1/2*w + 8],\ [2, 2, 1/2*w^2 - 3/2*w - 1],\ [2, 2, w + 3],\ [11, 11, -w^2 + 3*w + 7],\ [11, 11, -2*w - 1],\ [11, 11, -w^2 + w + 11],\ [27, 3, 3],\ [41, 41, 2*w + 5],\ [41, 41, -w^2 + 3*w + 3],\ [41, 41, -w^2 + w + 15],\ [43, 43, -3*w^2 + 11*w + 11],\ [47, 47, -w^2 - w + 5],\ [47, 47, w^2 - 5*w - 3],\ [47, 47, -2*w^2 + 4*w + 23],\ [59, 59, -w^2 + w + 13],\ [59, 59, w^2 - 3*w - 5],\ [59, 59, -2*w - 3],\ [97, 97, 7*w^2 - 11*w - 91],\ [97, 97, -2*w^2 - 8*w - 5],\ [97, 97, 5*w^2 - 19*w - 15],\ [107, 107, w^2 + 3*w - 1],\ [107, 107, -3*w^2 + 5*w + 37],\ [107, 107, w^2 - 5*w - 23],\ [113, 113, w^2 - 3*w - 1],\ [113, 113, w^2 - w - 17],\ [113, 113, -2*w - 7],\ [125, 5, -5],\ [127, 127, -w^2 - w - 1],\ [127, 127, 2*w^2 - 4*w - 29],\ [127, 127, -w^2 + 5*w - 3],\ [131, 131, -w^2 + 5*w - 1],\ [131, 131, 2*w^2 - 4*w - 27],\ [131, 131, w^2 + w - 1],\ [137, 137, 2*w^2 - 6*w - 5],\ [137, 137, -4*w - 11],\ [137, 137, 2*w^2 - 2*w - 31],\ [151, 151, -2*w^2 + 8*w + 3],\ [151, 151, 3*w^2 - 5*w - 41],\ [151, 151, -w^2 - 3*w - 3],\ [173, 173, 2*w^2 - 4*w - 25],\ [173, 173, w^2 + w - 3],\ [173, 173, -w^2 + 5*w + 1],\ [193, 193, -6*w - 17],\ [193, 193, 3*w^2 - 9*w - 7],\ [193, 193, 3*w^2 - 3*w - 47],\ [199, 199, w^2 + w - 7],\ [199, 199, 2*w^2 - 4*w - 21],\ [199, 199, -w^2 + 5*w + 5],\ [211, 211, 2*w - 7],\ [211, 211, w^2 - w - 3],\ [211, 211, -w^2 + 3*w + 15],\ [223, 223, w^2 - w - 7],\ [223, 223, w^2 - 3*w - 11],\ [223, 223, 2*w - 3],\ [257, 257, -2*w^2 - 4*w - 1],\ [257, 257, -3*w^2 + 13*w + 3],\ [257, 257, 5*w^2 - 9*w - 67],\ [269, 269, 2*w - 5],\ [269, 269, w^2 - 3*w - 13],\ [269, 269, w^2 - w - 5],\ [293, 293, -13*w^2 + 51*w + 35],\ [293, 293, -19*w^2 + 31*w + 247],\ [293, 293, 6*w^2 + 20*w + 9],\ [317, 317, 5*w^2 - 19*w - 17],\ [317, 317, 7*w^2 - 11*w - 89],\ [317, 317, 2*w^2 + 8*w + 3],\ [343, 7, -7],\ [379, 379, 3*w^2 - 11*w - 13],\ [379, 379, 4*w^2 - 6*w - 49],\ [379, 379, w^2 + 5*w + 1],\ [383, 383, -4*w - 5],\ [383, 383, -2*w^2 + 2*w + 25],\ [383, 383, 2*w^2 - 6*w - 11],\ [389, 389, 4*w^2 - 18*w - 13],\ [389, 389, -7*w^2 + 13*w + 83],\ [389, 389, 4*w^2 - 14*w - 11],\ [409, 409, 2*w - 11],\ [409, 409, w^2 - 3*w - 19],\ [409, 409, -w^2 + w - 1],\ [419, 419, 10*w^2 - 38*w - 31],\ [419, 419, -14*w^2 + 22*w + 181],\ [419, 419, 4*w^2 - 14*w - 17],\ [431, 431, -4*w^2 + 16*w + 13],\ [431, 431, 2*w^2 + 6*w - 1],\ [431, 431, -6*w^2 + 10*w + 75],\ [457, 457, -2*w^2 + 8*w + 9],\ [457, 457, 3*w^2 - 5*w - 35],\ [457, 457, w^2 + 3*w - 3],\ [557, 557, 5*w^2 - 9*w - 63],\ [557, 557, -3*w^2 + 13*w + 7],\ [557, 557, 2*w^2 + 4*w - 3],\ [563, 563, -9*w^2 + 35*w + 23],\ [563, 563, 13*w^2 - 21*w - 171],\ [563, 563, -4*w^2 - 14*w - 9],\ [601, 601, 5*w^2 - 17*w - 13],\ [601, 601, 6*w^2 - 8*w - 85],\ [601, 601, -w^2 - 9*w - 17],\ [613, 613, -2*w^2 + 15],\ [613, 613, 3*w^2 - 7*w - 31],\ [613, 613, 22*w^2 - 36*w - 285],\ [641, 641, 3*w^2 - 5*w - 43],\ [641, 641, -2*w^2 + 8*w + 1],\ [641, 641, -w^2 - 3*w - 5],\ [643, 643, 2*w^2 + 4*w - 1],\ [643, 643, 5*w^2 - 9*w - 65],\ [643, 643, -3*w^2 + 13*w + 5],\ [647, 647, 9*w^2 - 35*w - 27],\ [647, 647, 4*w^2 + 14*w + 5],\ [647, 647, 13*w^2 - 21*w - 167],\ [653, 653, -4*w^2 + 16*w + 7],\ [653, 653, 6*w^2 - 10*w - 81],\ [653, 653, -2*w^2 - 6*w - 5],\ [661, 661, -w^2 - 7*w - 13],\ [661, 661, -4*w^2 + 14*w + 9],\ [661, 661, 5*w^2 - 7*w - 71],\ [677, 677, -12*w^2 + 20*w + 155],\ [677, 677, -4*w^2 - 12*w - 3],\ [677, 677, -8*w^2 + 32*w + 21],\ [709, 709, -2*w^2 + 10*w - 3],\ [709, 709, 19*w^2 - 31*w - 249],\ [709, 709, 4*w^2 - 8*w - 55],\ [727, 727, -w^2 + 5*w + 21],\ [727, 727, -23*w^2 + 37*w + 301],\ [727, 727, -w^2 - w + 23],\ [733, 733, 2*w^2 + 2*w - 9],\ [733, 733, -2*w^2 + 10*w + 5],\ [733, 733, 4*w^2 - 8*w - 47],\ [739, 739, 2*w^2 - 6*w - 17],\ [739, 739, 2*w^2 - 2*w - 19],\ [739, 739, 4*w - 1],\ [773, 773, 8*w^2 - 12*w - 103],\ [773, 773, 6*w^2 - 22*w - 21],\ [773, 773, -2*w^2 - 10*w - 7],\ [809, 809, 4*w^2 + 16*w + 11],\ [809, 809, w^2 - 9*w - 7],\ [809, 809, 3*w^2 - w - 29],\ [821, 821, 3*w^2 + w - 23],\ [821, 821, 2*w^2 - 12*w - 9],\ [821, 821, 5*w^2 - 11*w - 51],\ [839, 839, 2*w^2 + 4*w - 7],\ [839, 839, 5*w^2 - 9*w - 59],\ [839, 839, 3*w^2 - 13*w - 11],\ [859, 859, w^2 + w - 11],\ [859, 859, 2*w^2 - 4*w - 17],\ [859, 859, w^2 - 5*w - 9],\ [881, 881, 4*w^2 - 14*w - 15],\ [881, 881, 5*w^2 - 7*w - 65],\ [881, 881, -w^2 - 7*w - 7],\ [887, 887, 5*w^2 - 7*w - 67],\ [887, 887, 4*w^2 - 14*w - 13],\ [887, 887, -w^2 - 7*w - 9],\ [907, 907, -3*w^2 - 11*w - 9],\ [907, 907, 10*w^2 - 16*w - 133],\ [907, 907, -7*w^2 + 27*w + 17],\ [911, 911, w^2 - 7*w - 7],\ [911, 911, 3*w^2 - 7*w - 27],\ [911, 911, 2*w^2 - 19],\ [919, 919, -3*w^2 - 5*w - 1],\ [919, 919, -4*w^2 + 18*w + 1],\ [919, 919, 7*w^2 - 13*w - 95],\ [947, 947, 4*w^2 - 6*w - 57],\ [947, 947, -3*w^2 + 11*w + 5],\ [947, 947, -w^2 - 5*w - 9],\ [967, 967, 8*w^2 - 30*w - 25],\ [967, 967, -3*w^2 - 13*w - 9],\ [967, 967, 11*w^2 - 17*w - 143],\ [991, 991, 2*w^2 - 8*w - 11],\ [991, 991, w^2 + 3*w - 5],\ [991, 991, 3*w^2 - 5*w - 33],\ [997, 997, 4*w^2 + 2*w - 27],\ [997, 997, 7*w^2 - 15*w - 75],\ [997, 997, -3*w^2 + 17*w + 11]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 1, -1, -2, -2, 2, -2, -6, 4, 6, 6, -8, -8, -12, -8, -12, 4, 6, -6, -8, 0, -4, -8, -6, 10, -12, 18, 12, -16, 4, -8, 0, 12, -2, -6, -4, -16, -20, 4, 18, 0, -6, -18, 16, 14, 0, -4, -8, 14, 10, -26, -6, 14, -2, -6, 22, 0, 14, -22, -14, 26, 24, -2, 2, -18, -10, 34, -12, -4, -20, -12, 16, 24, -10, 0, -6, 28, -34, 6, 32, -4, -16, -8, 8, -12, 2, 32, -6, 12, 18, -6, -12, 4, 36, -38, 46, -26, 22, -32, 10, 6, -8, 26, -40, -20, 16, -46, -6, 30, -34, -14, -18, 10, -48, -50, -18, -14, -12, -28, 38, 22, 24, 48, -36, 34, -16, 34, 40, -8, -12, 20, 14, 10, -30, 36, 30, 14, -26, -20, -22, 6, 6, 0, -16, -4, 34, -14, 28, 32, -36, 8, 12, -52, -28, -34, 42, -38, -10, -26, 46, 12, -44, 4, -32, -8, 16, 0, -44, 16, 38, 52, 18] 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, -1/2*w^2 + 1/2*w + 8])] = -1 AL_eigenvalues[ZF.ideal([2, 2, 1/2*w^2 - 3/2*w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]