/* 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, 0, -8, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([7, 7, w^3 - w^2 - 5*w + 7]) primes_array = [ [2, 2, -w^3 + w^2 + 5*w - 6],\ [7, 7, w^3 - w^2 - 5*w + 7],\ [7, 7, -w - 1],\ [7, 7, w - 1],\ [17, 17, w^2 - w - 5],\ [17, 17, w^2 + w - 5],\ [23, 23, -w - 3],\ [23, 23, w - 3],\ [25, 5, -w^3 + w^2 + 4*w - 3],\ [25, 5, -w^3 - w^2 + 4*w + 3],\ [41, 41, w^3 - 4*w - 1],\ [41, 41, -w^3 + 4*w - 1],\ [71, 71, -w^3 + 2*w^2 + 4*w - 9],\ [71, 71, w^3 + 2*w^2 - 4*w - 9],\ [73, 73, w^3 - w^2 - 5*w + 3],\ [73, 73, w^3 + w^2 - 5*w - 3],\ [79, 79, 2*w^2 - 2*w - 9],\ [79, 79, -2*w^3 + 8*w + 5],\ [81, 3, -3],\ [89, 89, -w^3 - 2*w^2 + 6*w + 13],\ [89, 89, w^3 - 2*w^2 - 6*w + 13],\ [97, 97, w^2 - 2*w - 5],\ [97, 97, 5*w^2 - 4*w - 19],\ [121, 11, -3*w^3 + w^2 + 12*w + 5],\ [121, 11, w^3 + w^2 - 6*w - 9],\ [127, 127, -2*w^3 - w^2 + 10*w + 3],\ [127, 127, 2*w^3 - w^2 - 10*w + 3],\ [151, 151, w^3 + 3*w^2 - 4*w - 9],\ [151, 151, -w^3 + 3*w^2 + 4*w - 9],\ [169, 13, -2*w^2 - w + 11],\ [169, 13, 2*w^2 - w - 11],\ [191, 191, 2*w^3 - 2*w^2 - 6*w + 3],\ [191, 191, -4*w^2 + 4*w + 17],\ [193, 193, 3*w^2 - w - 15],\ [193, 193, 2*w - 1],\ [193, 193, -2*w - 1],\ [193, 193, 3*w^2 + w - 15],\ [223, 223, w^3 - 6*w^2 - 9*w + 25],\ [223, 223, -5*w^2 + 3*w + 19],\ [223, 223, 2*w^3 + 5*w^2 - 11*w - 23],\ [223, 223, 2*w^3 + 3*w^2 - 8*w - 13],\ [233, 233, 3*w^3 + w^2 - 14*w - 13],\ [233, 233, w^3 - w^2 - 5*w + 1],\ [233, 233, -w^3 - w^2 + 5*w + 1],\ [233, 233, -w^3 + w^2 + 4*w + 1],\ [239, 239, w^3 - 5*w - 5],\ [239, 239, -w^3 + 5*w - 5],\ [241, 241, -2*w^3 - 7*w^2 + 14*w + 31],\ [241, 241, -2*w^3 - 3*w^2 + 12*w + 17],\ [257, 257, -4*w^2 + 2*w + 15],\ [257, 257, 2*w^3 + 6*w^2 - 12*w - 27],\ [263, 263, w^3 - w^2 - 2*w - 1],\ [263, 263, -w^3 - w^2 + 2*w - 1],\ [271, 271, 4*w^3 + 3*w^2 - 20*w - 23],\ [271, 271, w^2 + 2*w - 9],\ [271, 271, 3*w^2 - 3*w - 11],\ [271, 271, 3*w^2 - 2*w - 9],\ [281, 281, w^3 - w^2 - 7*w + 1],\ [281, 281, -w^3 + 6*w^2 + 8*w - 25],\ [281, 281, -w^3 + 4*w^2 + 6*w - 17],\ [281, 281, -w^3 + 4*w - 5],\ [289, 17, 3*w^2 - 13],\ [311, 311, -4*w^2 + w + 13],\ [311, 311, w^3 + 2*w^2 - 4*w - 11],\ [311, 311, -w^3 + 2*w^2 + 4*w - 11],\ [311, 311, -4*w^2 - w + 13],\ [313, 313, 3*w^3 - w^2 - 11*w - 3],\ [313, 313, w^3 - 3*w^2 - w + 11],\ [353, 353, 2*w^3 - w^2 - 9*w - 3],\ [353, 353, 5*w^2 - 3*w - 17],\ [359, 359, w^3 + 4*w^2 - 6*w - 15],\ [359, 359, -w^3 + 4*w^2 + 6*w - 15],\ [367, 367, -w^2 - w - 1],\ [367, 367, -2*w^3 - w^2 + 7*w + 1],\ [367, 367, 2*w^3 - w^2 - 7*w + 1],\ [367, 367, w^2 - w + 1],\ [401, 401, -2*w^3 + 8*w + 3],\ [401, 401, -w^3 + 2*w^2 + 3*w - 9],\ [401, 401, w^3 + 2*w^2 - 3*w - 9],\ [401, 401, -4*w^3 - 2*w^2 + 18*w + 17],\ [409, 409, 2*w^3 + 4*w^2 - 9*w - 19],\ [409, 409, 2*w^3 - 4*w^2 - 9*w + 19],\ [431, 431, w^3 - 6*w^2 - w + 19],\ [431, 431, w^3 + 6*w^2 - 7*w - 23],\ [433, 433, -6*w^2 + 6*w + 25],\ [433, 433, 2*w^3 - 4*w^2 - 4*w + 11],\ [439, 439, -w - 5],\ [439, 439, -w^3 + 3*w^2 + 4*w - 15],\ [439, 439, w^3 + 3*w^2 - 4*w - 15],\ [439, 439, w - 5],\ [457, 457, 2*w^3 + 2*w^2 - 7*w - 9],\ [457, 457, 3*w^3 + w^2 - 12*w - 9],\ [457, 457, 3*w^3 - 3*w^2 - 10*w + 5],\ [457, 457, -2*w^3 + 2*w^2 + 7*w - 9],\ [463, 463, 2*w^3 + w^2 - 9*w - 3],\ [463, 463, 2*w^3 - w^2 - 9*w + 3],\ [487, 487, -w^3 + w^2 + 6*w - 1],\ [487, 487, w^3 + w^2 - 6*w - 1],\ [503, 503, w^3 + 5*w^2 - 8*w - 23],\ [503, 503, w^3 + 3*w^2 - 6*w - 11],\ [503, 503, w^3 - 3*w^2 - 6*w + 11],\ [503, 503, -3*w^3 - 3*w^2 + 14*w + 19],\ [521, 521, -2*w^2 + 3*w + 11],\ [521, 521, 4*w^3 - 2*w^2 - 15*w - 3],\ [529, 23, -w^2 - 1],\ [569, 569, -w^3 + 5*w^2 - w - 19],\ [569, 569, w^3 - 3*w^2 - 3*w + 13],\ [569, 569, -w^3 - 3*w^2 + 3*w + 13],\ [569, 569, -3*w^3 + 3*w^2 + 9*w - 5],\ [577, 577, 2*w^3 - w^2 - 9*w - 1],\ [577, 577, -2*w^3 - w^2 + 9*w - 1],\ [593, 593, -w^3 + 4*w^2 + 5*w - 13],\ [593, 593, w^3 + 4*w^2 - 5*w - 13],\ [599, 599, -2*w^3 + 7*w + 1],\ [599, 599, 2*w^3 - 7*w + 1],\ [601, 601, -2*w^3 + 2*w^2 + 9*w - 5],\ [601, 601, 2*w^3 + 2*w^2 - 9*w - 5],\ [607, 607, w^3 + 4*w^2 - 5*w - 17],\ [607, 607, w^2 + 3*w - 1],\ [607, 607, w^2 - 3*w - 1],\ [607, 607, w^3 - 4*w^2 - 5*w + 17],\ [631, 631, -2*w^3 + 9*w - 1],\ [631, 631, 2*w^3 - 9*w - 1],\ [641, 641, -2*w^3 + w^2 + 8*w - 5],\ [641, 641, 2*w^3 - 8*w^2 - 2*w + 25],\ [641, 641, -2*w^2 + 4*w + 11],\ [641, 641, 2*w^3 + w^2 - 8*w - 5],\ [743, 743, -4*w^2 + w + 15],\ [743, 743, -4*w^2 - w + 15],\ [751, 751, -5*w^2 - 2*w + 15],\ [751, 751, -5*w^2 + 2*w + 15],\ [761, 761, w^3 + w^2 - 3*w - 9],\ [761, 761, -w^3 + w^2 + 3*w - 9],\ [769, 769, -2*w^3 + w^2 + 8*w - 3],\ [769, 769, 2*w^3 + w^2 - 8*w - 3],\ [809, 809, -w^3 + 7*w^2 + 10*w - 29],\ [809, 809, -w^3 + w^2 + 8*w - 9],\ [809, 809, w^3 + w^2 - 8*w - 9],\ [809, 809, w^3 - 3*w^2 - 8*w + 15],\ [823, 823, -w^3 + 2*w^2 + 2*w - 9],\ [823, 823, w^3 + 2*w^2 - 2*w - 9],\ [857, 857, 3*w^3 + w^2 - 14*w - 9],\ [857, 857, -3*w^3 + w^2 + 14*w - 9],\ [863, 863, 2*w^2 + 2*w - 13],\ [863, 863, 2*w^2 - 2*w - 13],\ [881, 881, 5*w^3 + 4*w^2 - 25*w - 29],\ [881, 881, w^3 + 4*w^2 - 7*w - 15],\ [911, 911, -2*w^3 + w^2 + 10*w - 1],\ [911, 911, 2*w^3 + w^2 - 10*w - 1],\ [919, 919, 3*w^3 - w^2 - 13*w - 1],\ [919, 919, -3*w^3 - w^2 + 13*w - 1],\ [929, 929, 2*w^3 - 3*w^2 - 9*w + 19],\ [929, 929, -2*w^3 - 3*w^2 + 9*w + 19],\ [937, 937, 2*w^3 - 4*w^2 - 11*w + 17],\ [937, 937, -2*w^3 - 4*w^2 + 11*w + 17],\ [961, 31, 4*w^2 - 15],\ [961, 31, 4*w^2 - 17],\ [967, 967, w^3 + 2*w^2 - 6*w - 5],\ [967, 967, -w^3 + 2*w^2 + 6*w - 5],\ [991, 991, w^2 - 3*w - 3],\ [991, 991, w^2 + 3*w - 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 1, 4, -4, 2, -2, -8, -8, 2, -2, -6, 6, 8, -8, 6, 6, 4, -4, -14, -10, -10, 10, -10, -2, -2, -8, -8, -8, -8, 22, -22, -20, 20, -6, 22, -22, 6, 16, 16, 16, -16, -26, 22, 22, -26, -16, -16, 26, -26, -6, -6, -4, 4, -8, 0, 0, -8, 6, -10, -10, 6, 34, -16, -8, 8, -16, -2, 2, 18, 18, 0, 0, -16, 28, -28, -16, -6, 14, -14, 6, -34, 34, 0, 0, 34, -34, 16, 32, -32, 16, -22, 26, -26, 22, 24, -24, -40, -40, 24, -8, -8, -24, 30, -30, 10, 18, 46, -46, -18, -14, -14, 26, 26, 32, -32, -26, -26, -32, 20, -20, -32, -28, 28, -14, -14, 14, 14, 8, 8, -16, -16, 22, -22, 10, -10, 26, 30, -30, -26, -44, 44, -26, 26, 16, -16, 18, 18, 40, 40, -40, 40, -14, 14, -2, -2, -62, -38, -40, -40, 36, -36] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([7,7,w^3-w^2-5*w+7])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]