/* 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([14, -10, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([8, 2, 2]) primes_array = [ [2, 2, w - 2],\ [2, 2, w^2 + 2*w - 5],\ [7, 7, w^2 + w - 7],\ [11, 11, -w^2 - w + 11],\ [11, 11, 2*w^2 + 2*w - 15],\ [11, 11, w^2 + w - 9],\ [13, 13, 2*w - 5],\ [17, 17, -w^2 - w + 5],\ [27, 3, -3],\ [29, 29, w^2 + w - 3],\ [37, 37, -2*w^2 + 15],\ [43, 43, 3*w^2 + w - 27],\ [49, 7, -w^2 + w + 3],\ [67, 67, 2*w^2 + 2*w - 17],\ [71, 71, 2*w - 1],\ [79, 79, 3*w^2 + w - 25],\ [83, 83, w^2 + 3*w - 5],\ [89, 89, -4*w^2 - 4*w + 31],\ [89, 89, -2*w^2 + 17],\ [89, 89, 2*w^2 + 2*w - 19],\ [97, 97, 2*w^2 + 2*w - 13],\ [101, 101, 2*w^2 + 2*w - 9],\ [101, 101, 3*w^2 + 3*w - 31],\ [101, 101, w^2 + 3*w - 3],\ [103, 103, -w^2 + 3*w + 1],\ [109, 109, -w^2 + w + 15],\ [125, 5, -5],\ [127, 127, -w^2 - 3*w + 15],\ [137, 137, -2*w - 5],\ [137, 137, -2*w^2 - 4*w + 13],\ [137, 137, -2*w^2 + 2*w + 9],\ [139, 139, -4*w + 9],\ [149, 149, -2*w - 1],\ [157, 157, -2*w^2 + 23],\ [163, 163, -w^2 + w - 1],\ [169, 13, 5*w^2 + w - 41],\ [173, 173, -5*w^2 - 9*w + 23],\ [173, 173, w^2 - w - 9],\ [179, 179, w^2 + w - 1],\ [191, 191, 3*w^2 + 3*w - 25],\ [193, 193, -5*w^2 - 3*w + 43],\ [197, 197, 2*w^2 - 4*w - 3],\ [199, 199, w^2 - w - 11],\ [211, 211, -w^2 - 3*w + 11],\ [223, 223, 3*w^2 + 5*w - 19],\ [227, 227, 2*w^2 + 2*w - 23],\ [229, 229, w^2 + 3*w - 13],\ [239, 239, -9*w^2 - 15*w + 43],\ [241, 241, -5*w^2 - 5*w + 39],\ [251, 251, 2*w^2 - 2*w - 3],\ [269, 269, -4*w^2 - 4*w + 29],\ [271, 271, 6*w^2 - 47],\ [277, 277, -2*w^2 + 2*w + 29],\ [277, 277, 4*w^2 + 8*w - 23],\ [277, 277, 7*w^2 + 5*w - 61],\ [281, 281, -6*w^2 - 4*w + 51],\ [283, 283, 4*w^2 + 4*w - 43],\ [283, 283, 3*w^2 + 3*w - 29],\ [283, 283, -2*w^2 + 4*w + 1],\ [289, 17, 3*w^2 + w - 23],\ [307, 307, 7*w^2 + 5*w - 69],\ [307, 307, -6*w^2 - 2*w + 51],\ [307, 307, -8*w + 13],\ [313, 313, 2*w^2 - 11],\ [313, 313, -5*w^2 - 5*w + 37],\ [313, 313, w^2 - 3*w + 5],\ [317, 317, -7*w^2 - 5*w + 59],\ [331, 331, -6*w + 11],\ [337, 337, -4*w + 13],\ [337, 337, 6*w^2 + 4*w - 59],\ [337, 337, w^2 - 3*w - 3],\ [347, 347, 8*w^2 + 14*w - 43],\ [353, 353, 5*w^2 + w - 43],\ [367, 367, 2*w^2 - 9],\ [367, 367, 3*w^2 + 3*w - 19],\ [367, 367, w^2 + w - 15],\ [379, 379, 7*w^2 + 5*w - 67],\ [383, 383, -3*w^2 - 7*w + 15],\ [383, 383, -6*w^2 - 2*w + 57],\ [383, 383, w^2 - 5*w + 9],\ [389, 389, -2*w^2 - 4*w + 25],\ [397, 397, 2*w^2 - 2*w - 5],\ [409, 409, 8*w^2 + 2*w - 67],\ [419, 419, -2*w - 9],\ [433, 433, 6*w^2 + 2*w - 55],\ [439, 439, 2*w^2 + 2*w - 5],\ [449, 449, 2*w^2 + 4*w - 5],\ [457, 457, 2*w^2 + 6*w - 33],\ [467, 467, 15*w^2 + 7*w - 135],\ [487, 487, -4*w^2 + 6*w + 15],\ [491, 491, -4*w^2 - 2*w + 41],\ [491, 491, -2*w^2 + 6*w + 1],\ [491, 491, -6*w^2 - 12*w + 29],\ [499, 499, 4*w^2 - 33],\ [499, 499, 4*w^2 + 6*w - 47],\ [499, 499, w^2 + 5*w - 13],\ [509, 509, 2*w^2 + 4*w - 17],\ [521, 521, -w^2 + w - 3],\ [523, 523, -2*w^2 - 6*w + 11],\ [541, 541, -6*w^2 - 10*w + 27],\ [557, 557, 5*w^2 - w - 37],\ [569, 569, -8*w^2 - 6*w + 69],\ [571, 571, 5*w^2 + 3*w - 41],\ [577, 577, 3*w^2 - w - 23],\ [593, 593, 4*w^2 - 29],\ [599, 599, 3*w^2 + w - 33],\ [601, 601, w^2 + 5*w - 19],\ [607, 607, 5*w^2 + 7*w - 25],\ [607, 607, 2*w^2 - 25],\ [607, 607, -10*w^2 - 18*w + 53],\ [617, 617, 7*w^2 + 11*w - 37],\ [619, 619, 4*w^2 + 4*w - 27],\ [631, 631, w^2 - 5*w + 1],\ [641, 641, 4*w^2 + 4*w - 39],\ [641, 641, 4*w^2 - 45],\ [641, 641, 4*w^2 + 2*w - 31],\ [643, 643, w^2 - 3*w - 5],\ [647, 647, 2*w^2 + 4*w - 23],\ [659, 659, 2*w^2 + 4*w - 19],\ [661, 661, 2*w^2 + 2*w - 25],\ [673, 673, -7*w^2 - 5*w + 65],\ [677, 677, -5*w^2 - 7*w + 27],\ [683, 683, -9*w^2 - 5*w + 79],\ [691, 691, 5*w^2 + w - 45],\ [701, 701, w^2 + 5*w - 15],\ [709, 709, 5*w^2 + 5*w - 51],\ [709, 709, 3*w^2 + w - 11],\ [709, 709, 2*w^2 + 6*w - 5],\ [719, 719, 3*w^2 - 7*w - 1],\ [733, 733, 4*w - 1],\ [739, 739, -5*w^2 - 5*w + 41],\ [743, 743, 6*w^2 + 8*w - 37],\ [743, 743, 2*w^2 + 6*w - 17],\ [743, 743, 4*w^2 - 2*w - 27],\ [751, 751, w^2 + 5*w - 17],\ [757, 757, -5*w^2 - w + 53],\ [757, 757, 8*w^2 + 2*w - 69],\ [757, 757, -w^2 - 3*w - 3],\ [761, 761, 2*w - 11],\ [769, 769, -w^2 + 3*w + 19],\ [769, 769, 2*w^2 + 6*w - 9],\ [769, 769, -4*w^2 + 2*w + 51],\ [773, 773, 3*w^2 - w - 17],\ [787, 787, -4*w^2 - 8*w + 25],\ [797, 797, -5*w^2 - w + 47],\ [797, 797, w^2 + w - 17],\ [797, 797, -2*w^2 - 8*w + 15],\ [811, 811, 3*w^2 + 5*w - 23],\ [823, 823, -2*w^2 + 10*w - 15],\ [827, 827, 5*w^2 + w - 39],\ [829, 829, 8*w^2 + 8*w - 85],\ [839, 839, 3*w^2 - 11*w + 5],\ [841, 29, 5*w^2 + 3*w - 51],\ [857, 857, -8*w + 15],\ [859, 859, -4*w^2 + 41],\ [863, 863, 7*w^2 + 13*w - 39],\ [877, 877, 2*w^2 - 8*w + 3],\ [877, 877, -11*w^2 - 21*w + 55],\ [877, 877, -w^2 + 7*w - 5],\ [911, 911, 10*w^2 + 8*w - 99],\ [937, 937, 5*w^2 - w - 57],\ [967, 967, 3*w^2 + w - 17],\ [971, 971, 4*w - 15],\ [977, 977, -8*w^2 - 4*w + 69],\ [983, 983, -w^2 - w - 3],\ [983, 983, -10*w^2 - 6*w + 87],\ [983, 983, 3*w^2 - 3*w - 5],\ [997, 997, 3*w^2 + 5*w - 39]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, -4, 0, 2, -2, -4, 2, 8, -10, -8, 12, -2, 10, 0, -8, -4, 2, 6, 14, -2, 12, -16, -2, 8, 18, 6, -12, -14, -22, 18, 14, -6, 18, -4, 14, -10, 6, -16, -20, 26, 20, 8, -14, 12, 8, 24, 8, -2, 30, 12, 16, 18, 24, -8, 18, 4, 6, 6, -18, -12, -18, 2, -2, 2, 26, -24, 34, 10, 14, 22, -30, 18, -28, 8, 16, 10, 8, 8, 24, 24, -12, 38, 8, 6, 0, -2, -26, -26, -16, -24, -32, -32, -24, -14, -18, 16, 14, -44, -2, 2, -6, 14, 14, 18, 40, 30, 32, -8, 40, -30, 2, 8, -2, 30, -22, 12, -8, -10, -34, -46, 12, 6, 36, 0, 52, -40, 10, 0, -6, 38, 40, -4, -24, -20, 2, -2, 34, 42, 14, 2, 14, -48, -14, -14, 30, 26, 6, 16, 22, 14, 0, 54, -10, -20, 4, 14, -22, -38, -4, 22, 28, -48, 6, 48, -36, 24, -6] 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 - 2])] = -1 AL_eigenvalues[ZF.ideal([2, 2, w^2 + 2*w - 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]