/* 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([5, 5, -4, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([29, 29, w^3 - 4*w - 1]) primes_array = [ [5, 5, w],\ [5, 5, w^3 - 2*w^2 - 2*w + 3],\ [11, 11, -w^2 + 4],\ [11, 11, w^2 - 2*w - 3],\ [16, 2, 2],\ [29, 29, w^3 - 4*w - 1],\ [29, 29, w^3 - 3*w^2 - w + 4],\ [41, 41, w^3 - 2*w^2 - w + 4],\ [41, 41, -w^3 + w^2 + 2*w + 2],\ [59, 59, -2*w^3 + 4*w^2 + 4*w - 7],\ [59, 59, -3*w^2 + 2*w + 7],\ [61, 61, -w^3 + 4*w^2 - 6],\ [61, 61, w^3 + w^2 - 5*w - 3],\ [71, 71, w^3 + w^2 - 4*w - 6],\ [71, 71, 3*w^2 - 2*w - 8],\ [71, 71, 3*w^2 - 4*w - 7],\ [71, 71, w^3 - 4*w^2 + w + 8],\ [79, 79, -2*w^3 + 3*w^2 + 5*w - 2],\ [79, 79, 2*w^2 - 3*w - 7],\ [79, 79, 2*w^2 - w - 8],\ [79, 79, -2*w^3 + 3*w^2 + 5*w - 4],\ [81, 3, -3],\ [89, 89, -w - 3],\ [89, 89, w - 4],\ [101, 101, w^3 - 6*w - 2],\ [101, 101, 2*w^3 - 3*w^2 - 5*w + 3],\ [101, 101, -w^3 + 3*w^2 + 3*w - 7],\ [109, 109, -3*w^2 + 5*w + 4],\ [109, 109, -2*w^3 + w^2 + 6*w + 4],\ [121, 11, 3*w^2 - 3*w - 8],\ [139, 139, -w^3 - w^2 + 6*w + 3],\ [139, 139, w^3 - 4*w^2 - w + 7],\ [149, 149, -2*w^3 + 6*w^2 + w - 11],\ [149, 149, 2*w^3 - 7*w - 6],\ [151, 151, -w^3 + 2*w^2 + 4*w - 4],\ [151, 151, w^3 - w^2 - 5*w + 1],\ [169, 13, -4*w^2 + 5*w + 11],\ [169, 13, 3*w^3 - 6*w^2 - 7*w + 8],\ [181, 181, w^3 + w^2 - 4*w - 7],\ [181, 181, -2*w^2 + 5*w + 1],\ [181, 181, 3*w^3 - 3*w^2 - 9*w + 2],\ [181, 181, -w^3 + 4*w^2 - w - 9],\ [191, 191, w^3 - 5*w + 1],\ [191, 191, -w^3 + 3*w^2 + 2*w - 3],\ [199, 199, -2*w^3 + 2*w^2 + 5*w + 4],\ [199, 199, -2*w^3 + 9*w + 4],\ [229, 229, 2*w^2 - 5*w - 4],\ [229, 229, -4*w^2 + 5*w + 8],\ [241, 241, -3*w^3 + 7*w^2 + 5*w - 12],\ [241, 241, -3*w^3 + 2*w^2 + 10*w + 3],\ [269, 269, -w^3 + 6*w^2 - 3*w - 13],\ [269, 269, w^3 + 3*w^2 - 6*w - 11],\ [271, 271, 2*w^3 - 2*w^2 - 7*w + 3],\ [271, 271, -2*w^3 + 4*w^2 + 5*w - 4],\ [289, 17, w^3 - 6*w^2 + 2*w + 11],\ [289, 17, w^3 + 3*w^2 - 7*w - 8],\ [311, 311, -2*w^3 + w^2 + 5*w + 4],\ [311, 311, 2*w^3 - 5*w^2 - w + 8],\ [331, 331, 3*w^3 - 3*w^2 - 11*w - 3],\ [331, 331, -3*w^3 + 6*w^2 + 8*w - 14],\ [349, 349, -3*w^3 + 6*w^2 + 6*w - 8],\ [349, 349, 3*w^3 - 3*w^2 - 9*w + 1],\ [359, 359, -2*w^3 - w^2 + 7*w + 8],\ [359, 359, -2*w^3 + 6*w^2 + w - 12],\ [359, 359, 2*w^3 - 7*w - 7],\ [359, 359, -2*w^3 + 7*w^2 - w - 12],\ [361, 19, 4*w^2 - 4*w - 11],\ [361, 19, -4*w^2 + 4*w + 9],\ [389, 389, -w^3 + 4*w^2 - w - 11],\ [389, 389, w^3 + w^2 - 4*w - 9],\ [401, 401, w^2 - 8],\ [401, 401, w^2 - 2*w - 7],\ [409, 409, -3*w^2 + 5*w + 9],\ [409, 409, -3*w^3 + w^2 + 12*w + 4],\ [409, 409, -w^3 + w^2 + 6*w + 1],\ [409, 409, 3*w^2 - w - 11],\ [419, 419, w^3 - 7*w - 3],\ [419, 419, -w^3 + 3*w^2 + 4*w - 9],\ [431, 431, -2*w^3 + 2*w^2 + 7*w - 4],\ [431, 431, w^3 + 2*w^2 - 7*w - 4],\ [439, 439, -2*w^3 + 5*w^2 + 2*w - 11],\ [439, 439, 2*w^3 - w^2 - 6*w - 6],\ [449, 449, w^3 + 3*w^2 - 7*w - 9],\ [449, 449, w^3 - 6*w^2 + 5*w + 11],\ [449, 449, 3*w^3 - 7*w^2 - 3*w + 8],\ [449, 449, -w^3 + 6*w^2 - 2*w - 12],\ [461, 461, -3*w^3 + 8*w^2 + 4*w - 18],\ [461, 461, 3*w^3 - 4*w^2 - 5*w - 1],\ [479, 479, -w^3 + 5*w^2 - 2*w - 16],\ [479, 479, 2*w^3 - 4*w^2 - w - 1],\ [491, 491, -w^3 + 7*w^2 - w - 18],\ [491, 491, w^3 + 2*w^2 - 5*w - 11],\ [491, 491, -w^3 + 5*w^2 - 2*w - 13],\ [491, 491, w^3 + 4*w^2 - 10*w - 13],\ [499, 499, 3*w^3 - 4*w^2 - 8*w + 3],\ [499, 499, -w^3 + 4*w^2 + 2*w - 6],\ [499, 499, -w^3 - w^2 + 7*w + 1],\ [499, 499, 3*w^3 - 5*w^2 - 7*w + 6],\ [529, 23, 4*w^3 - 3*w^2 - 13*w - 1],\ [529, 23, w^3 + 4*w^2 - 9*w - 8],\ [569, 569, -3*w^3 + 7*w^2 + 4*w - 14],\ [569, 569, 3*w^3 - 4*w^2 - 7*w + 1],\ [569, 569, 3*w^3 - 5*w^2 - 6*w + 7],\ [569, 569, w^3 - 4*w^2 + 4*w + 7],\ [571, 571, -w^3 + 7*w^2 - w - 17],\ [571, 571, w^3 + 4*w^2 - 10*w - 12],\ [599, 599, 3*w^3 - 6*w^2 - 5*w + 7],\ [599, 599, 3*w^3 - 3*w^2 - 8*w + 1],\ [619, 619, -w^3 + 3*w^2 + 4*w - 7],\ [619, 619, 2*w^3 - 6*w^2 - w + 13],\ [619, 619, -w^3 + 3*w^2 - 2*w - 6],\ [619, 619, w^3 - 7*w - 1],\ [641, 641, 3*w^3 - 3*w^2 - 7*w + 1],\ [641, 641, -3*w^3 + 6*w^2 + 4*w - 6],\ [659, 659, -2*w^3 + 5*w^2 + 6*w - 7],\ [659, 659, -2*w^3 + w^2 + 10*w - 2],\ [661, 661, 2*w^3 - 4*w^2 - w + 6],\ [661, 661, w^3 + 2*w^2 - 5*w - 12],\ [701, 701, -w^3 + 3*w^2 - w - 9],\ [701, 701, -2*w^3 + w^2 + 9*w - 1],\ [701, 701, 2*w^3 - 8*w - 1],\ [701, 701, w^3 - 2*w - 8],\ [709, 709, 2*w^3 - 2*w^2 - 9*w + 1],\ [709, 709, w^3 - w^2 + w - 2],\ [719, 719, -5*w^2 + 4*w + 14],\ [719, 719, -5*w^2 + 6*w + 13],\ [739, 739, 4*w^3 - 6*w^2 - 11*w + 7],\ [739, 739, -4*w^3 + 6*w^2 + 11*w - 6],\ [751, 751, -w^3 + 7*w^2 - 4*w - 16],\ [751, 751, -w^3 - 4*w^2 + 7*w + 14],\ [769, 769, w^3 - 3*w^2 - w + 11],\ [769, 769, -w^3 + 4*w + 8],\ [811, 811, -w^3 + 4*w^2 - 14],\ [811, 811, -w^3 - w^2 + 5*w + 11],\ [829, 829, -w^3 + 2*w^2 - w - 6],\ [829, 829, w^2 + 3*w - 1],\ [829, 829, 3*w^3 - 13*w - 6],\ [829, 829, w^3 - w^2 - 6],\ [841, 29, 5*w^2 - 5*w - 14],\ [859, 859, -w^3 + 6*w^2 - 11],\ [859, 859, -3*w^3 + 5*w^2 + 8*w - 2],\ [881, 881, -3*w^3 + w^2 + 11*w + 2],\ [881, 881, -3*w^3 + 8*w^2 + 4*w - 11],\ [911, 911, -2*w^2 - w + 11],\ [911, 911, 2*w^2 - 5*w - 8],\ [919, 919, w^3 - 5*w^2 - w + 8],\ [919, 919, -w^3 - 2*w^2 + 8*w + 3],\ [941, 941, 2*w^3 + 2*w^2 - 11*w - 7],\ [941, 941, -2*w^3 + 8*w^2 + w - 14],\ [961, 31, -2*w^2 + 2*w + 11],\ [961, 31, 5*w^2 - 5*w - 13],\ [971, 971, w^3 - 2*w^2 - 3*w - 3],\ [971, 971, -w^3 + w^2 + 4*w - 7],\ [991, 991, -w^3 + 4*w^2 + 2*w - 16],\ [991, 991, w^3 + 3*w^2 - 5*w - 13],\ [991, 991, -w^3 + 6*w^2 - 4*w - 14],\ [991, 991, 2*w^3 + 3*w^2 - 10*w - 12]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 4, -2, 3, 3, -1, 0, -3, 2, 0, 0, -12, -2, -2, -8, -3, 3, -10, -15, -15, 5, 8, -10, 0, -8, -7, -3, 15, -5, -3, -5, 20, 0, 20, -2, 8, 10, -5, -23, -12, -7, -18, 2, 17, 5, 20, -10, -10, 18, 3, -10, 0, 28, 8, 25, 10, 3, -2, 7, 32, 10, 20, 35, 35, -25, 0, -12, -17, -10, 5, -27, 38, 30, -30, 20, -25, 30, 5, -33, 32, 15, -20, 30, 40, -25, 30, -27, 3, -30, -25, 12, -7, -2, 42, 30, 20, 25, 10, -20, -20, -15, -30, 0, 0, 17, 7, 0, -5, 30, -30, 30, -15, 22, 47, 40, 0, -13, -18, 32, -18, -18, 2, -25, 5, -20, 15, -40, 10, 8, 8, -50, 50, -8, 22, -10, 15, 35, -10, 8, -20, -20, -32, 18, 53, -12, 0, -25, 18, 33, -43, 2, 3, 3, 52, 7, 2, 32] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([29, 29, w^3 - 4*w - 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]