/* 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([2, 0, -4, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([34, 34, w^2 - w - 4]) primes_array = [ [2, 2, w],\ [17, 17, -w^2 - w + 3],\ [17, 17, -w^3 - w^2 + 3*w + 1],\ [17, 17, w^3 - w^2 - 3*w + 1],\ [17, 17, w^2 - w - 3],\ [31, 31, w^3 + w^2 - 2*w - 3],\ [31, 31, -w^3 + w^2 + 4*w - 1],\ [31, 31, w^3 + w^2 - 4*w - 1],\ [31, 31, -w^3 + w^2 + 2*w - 3],\ [47, 47, -2*w^3 + w^2 + 5*w - 1],\ [47, 47, 2*w^3 + w^2 - 6*w - 1],\ [47, 47, -2*w^3 + w^2 + 6*w - 1],\ [47, 47, 2*w^3 + w^2 - 5*w - 1],\ [49, 7, w^2 + 1],\ [49, 7, -2*w^2 + 3],\ [79, 79, -w^3 - w^2 + 4*w - 1],\ [79, 79, -w^3 + w^2 + 2*w - 5],\ [79, 79, w^3 + w^2 - 2*w - 5],\ [79, 79, w^3 - w^2 - 4*w - 1],\ [81, 3, -3],\ [97, 97, -2*w^3 + 8*w + 1],\ [97, 97, -2*w^3 + 4*w - 1],\ [97, 97, -2*w^3 + 4*w + 1],\ [97, 97, 2*w^3 - 8*w + 1],\ [113, 113, w^3 - w^2 - w + 3],\ [113, 113, 2*w^3 - w^2 - 7*w + 1],\ [113, 113, 2*w^3 + w^2 - 7*w - 1],\ [113, 113, w^3 + w^2 - w - 3],\ [127, 127, 2*w^3 + 2*w^2 - 6*w - 3],\ [127, 127, 2*w^2 - 2*w - 5],\ [127, 127, 2*w^2 + 2*w - 5],\ [127, 127, -2*w^3 + 2*w^2 + 6*w - 3],\ [191, 191, 2*w^3 - 9*w - 3],\ [191, 191, -w^3 + 3*w^2 + 3*w - 5],\ [191, 191, -w^3 - 3*w^2 + 3*w + 5],\ [191, 191, -2*w^3 + 9*w - 3],\ [193, 193, -4*w^3 - w^2 + 12*w + 1],\ [193, 193, 3*w^3 - w^2 - 11*w + 1],\ [193, 193, -3*w^3 - w^2 + 11*w + 1],\ [193, 193, -w^3 + 2*w^2 + 5*w - 7],\ [223, 223, 3*w^3 - w^2 - 10*w + 1],\ [223, 223, w^3 - 5*w - 5],\ [223, 223, -w^3 + 5*w - 5],\ [223, 223, -3*w^3 - w^2 + 10*w + 1],\ [239, 239, -2*w^2 + w - 1],\ [239, 239, -w^3 - 2*w^2 + 3*w + 9],\ [239, 239, w^3 - 2*w^2 - 3*w + 9],\ [239, 239, -2*w^2 - w - 1],\ [241, 241, -w^3 + w^2 + 2*w - 7],\ [241, 241, -w^3 - 2*w^2 + w + 5],\ [241, 241, w^3 - 2*w^2 - w + 5],\ [241, 241, w^3 + w^2 - 2*w - 7],\ [257, 257, -w^3 - 3*w^2 + w + 7],\ [257, 257, -2*w^2 + 3*w + 5],\ [257, 257, -2*w^2 - 3*w + 5],\ [257, 257, w^3 - 3*w^2 - w + 7],\ [271, 271, 3*w^3 - 10*w + 3],\ [271, 271, w^3 + 3],\ [271, 271, -w^3 + 3],\ [271, 271, -3*w^3 + 10*w + 3],\ [337, 337, -w^3 + w^2 + w - 5],\ [337, 337, -2*w^3 + w^2 + 7*w + 1],\ [337, 337, 2*w^3 + w^2 - 7*w + 1],\ [337, 337, w^3 + w^2 - w - 5],\ [353, 353, -w^3 + 6*w - 1],\ [353, 353, 3*w^3 - 8*w + 1],\ [353, 353, 3*w^3 - 8*w - 1],\ [353, 353, w^3 - 6*w - 1],\ [367, 367, -2*w^3 + w^2 + 8*w + 1],\ [367, 367, -2*w^3 + w^2 + 4*w - 5],\ [367, 367, 2*w^3 + w^2 - 4*w - 5],\ [367, 367, 2*w^3 + w^2 - 8*w + 1],\ [383, 383, -w^3 - w^2 + 3*w - 3],\ [383, 383, w^2 - w - 7],\ [383, 383, w^2 + w - 7],\ [383, 383, w^3 - w^2 - 3*w - 3],\ [401, 401, 3*w^3 - w^2 - 9*w - 1],\ [401, 401, w^3 - w^2 - 4*w + 7],\ [401, 401, w^3 + w^2 - 4*w - 7],\ [401, 401, -3*w^3 - w^2 + 9*w - 1],\ [431, 431, 2*w^2 + 2*w - 7],\ [431, 431, 2*w^3 - 2*w^2 - 6*w + 1],\ [431, 431, -2*w^3 - 2*w^2 + 6*w + 1],\ [431, 431, 2*w^2 - 2*w - 7],\ [433, 433, w^3 - 2*w - 5],\ [433, 433, w^3 - 4*w - 5],\ [433, 433, -w^3 + 4*w - 5],\ [433, 433, -w^3 + 2*w - 5],\ [449, 449, 3*w^3 + 3*w^2 - 9*w - 5],\ [449, 449, w^2 + 4*w - 1],\ [449, 449, -w^2 + 4*w + 1],\ [449, 449, -3*w^3 + 3*w^2 + 9*w - 5],\ [463, 463, -w^3 + w^2 + 3*w - 7],\ [463, 463, -w^2 - w - 3],\ [463, 463, -w^2 + w - 3],\ [463, 463, w^3 + w^2 - 3*w - 7],\ [479, 479, 2*w^3 - w^2 - 9*w + 3],\ [479, 479, 3*w^3 - w^2 - 7*w + 1],\ [479, 479, -3*w^3 - w^2 + 7*w + 1],\ [479, 479, -2*w^3 - w^2 + 9*w + 3],\ [529, 23, -w^2 - 3],\ [529, 23, w^2 - 7],\ [577, 577, -3*w^3 + 11*w - 5],\ [577, 577, 3*w^3 + w^2 - 12*w - 3],\ [577, 577, -3*w^3 + w^2 + 12*w - 3],\ [577, 577, 3*w^3 - 11*w - 5],\ [593, 593, -2*w^3 - 3*w^2 + 5*w + 1],\ [593, 593, 2*w^3 + 4*w^2 - 6*w - 9],\ [593, 593, -2*w^3 + 4*w^2 + 6*w - 9],\ [593, 593, 2*w^3 - 3*w^2 - 5*w + 1],\ [607, 607, -w^3 + 2*w^2 + 7*w - 3],\ [607, 607, 4*w^3 + 2*w^2 - 11*w - 5],\ [607, 607, -4*w^3 + 2*w^2 + 11*w - 5],\ [607, 607, -3*w^2 - 2*w + 9],\ [625, 5, -5],\ [641, 641, w^3 - 4*w^2 - 4*w + 7],\ [641, 641, 3*w^3 - w^2 - 9*w - 3],\ [641, 641, -3*w^3 - w^2 + 9*w - 3],\ [641, 641, -w^3 - 4*w^2 + 4*w + 7],\ [673, 673, 2*w^3 - 2*w^2 - 7*w + 1],\ [673, 673, -2*w^3 + w^2 + w - 3],\ [673, 673, -2*w^3 - w^2 + w + 3],\ [673, 673, 2*w^3 + 2*w^2 - 7*w - 1],\ [719, 719, -w^3 - 4*w^2 + 4*w + 3],\ [719, 719, w^3 - w^2 + 5],\ [719, 719, -w^3 - w^2 + 5],\ [719, 719, -w^3 + 4*w^2 + 4*w - 3],\ [751, 751, 3*w^3 - 3*w^2 - 8*w + 3],\ [751, 751, w^3 + 3*w^2 - 6*w - 9],\ [751, 751, -w^3 + 3*w^2 + 6*w - 9],\ [751, 751, -3*w^3 - 3*w^2 + 8*w + 3],\ [769, 769, w^3 - 4*w^2 - 4*w + 9],\ [769, 769, w^3 + 4*w^2 - 2*w - 7],\ [769, 769, -w^3 + 4*w^2 + 2*w - 7],\ [769, 769, w^3 + 4*w^2 - 4*w - 9],\ [863, 863, -w^3 + 4*w^2 + 3*w - 9],\ [863, 863, 4*w^2 - w - 7],\ [863, 863, 4*w^2 + w - 7],\ [863, 863, w^3 + 4*w^2 - 3*w - 9],\ [881, 881, 2*w^2 - 3*w - 7],\ [881, 881, 3*w^3 + 2*w^2 - 9*w - 1],\ [881, 881, 3*w^3 - 2*w^2 - 9*w + 1],\ [881, 881, 2*w^2 + 3*w - 7],\ [911, 911, -w^3 - w^2 + 7*w + 1],\ [911, 911, 4*w^3 - w^2 - 11*w + 3],\ [911, 911, 4*w^3 + w^2 - 11*w - 3],\ [911, 911, w^3 - w^2 - 7*w + 1],\ [929, 929, 2*w^3 - 10*w + 3],\ [929, 929, 4*w^3 - 10*w - 3],\ [929, 929, -4*w^3 + 10*w - 3],\ [929, 929, 2*w^3 - 10*w - 3],\ [977, 977, -4*w^3 + 3*w^2 + 11*w - 11],\ [977, 977, 4*w^3 + 3*w^2 - 16*w - 9],\ [977, 977, -2*w^3 + 5*w^2 + 5*w - 15],\ [977, 977, 4*w^3 + 3*w^2 - 11*w - 11],\ [991, 991, -4*w^3 + 11*w + 1],\ [991, 991, w^3 - 7*w - 1],\ [991, 991, -w^3 + 7*w - 1],\ [991, 991, 4*w^3 - 11*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 3, -1, 3, 6, 5, -7, 5, 2, 0, -12, -3, -3, 2, -1, -1, -4, 2, -10, 1, 5, -16, 8, -16, 6, -12, -12, 9, 20, 2, 2, -13, -3, 24, 12, -6, -16, 23, -16, -22, 20, 8, -4, -28, 24, -12, -15, -6, 20, 20, -4, -1, -6, 6, 15, -3, 32, 14, -13, -16, -13, 8, 26, -13, 18, 0, -9, 0, 8, -19, -22, 32, 9, 21, -9, 24, 18, 0, -15, 0, -24, -30, 30, 18, 8, -25, 14, 38, 6, 27, -21, -24, -16, -13, -4, -22, 6, -18, -36, -21, -25, -10, -4, -16, -7, -7, 0, 6, -39, 0, 8, 8, -19, 20, -37, -12, -30, -42, 33, 41, 38, -34, 17, 27, 39, -21, -18, -43, 41, 32, -28, 8, -13, -28, 41, 27, -24, 6, 24, -15, 12, 30, -18, -48, 48, -9, 9, 57, -54, 3, -51, -18, -18, 36, 48, -25, -4, 47, -40] 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])] = 1 AL_eigenvalues[ZF.ideal([17, 17, -w^3 - w^2 + 3*w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]