/* 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([9, -8, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 3, w^2 + w - 6]) primes_array = [ [3, 3, -w + 3],\ [3, 3, w - 2],\ [5, 5, w^2 + w - 5],\ [8, 2, 2],\ [13, 13, w + 2],\ [13, 13, -2*w + 5],\ [13, 13, -w^2 - w + 4],\ [19, 19, -w^2 + w + 4],\ [23, 23, -w^2 - w + 7],\ [25, 5, w^2 - 2*w - 1],\ [29, 29, w^2 - 5],\ [31, 31, w^2 + w - 8],\ [41, 41, w^2 + w - 11],\ [47, 47, w^2 + 2*w - 1],\ [59, 59, w^2 + w - 1],\ [61, 61, -w^2 + 5*w - 7],\ [67, 67, 2*w^2 - 13],\ [89, 89, -2*w^2 + w + 20],\ [89, 89, 5*w^2 + 8*w - 19],\ [89, 89, w^2 + 2*w - 7],\ [101, 101, -w - 5],\ [101, 101, w^2 - 2*w - 4],\ [101, 101, -2*w - 1],\ [103, 103, -3*w^2 - 2*w + 20],\ [107, 107, 2*w^2 + 3*w - 10],\ [109, 109, -3*w^2 - 3*w + 17],\ [127, 127, 2*w^2 - w - 14],\ [131, 131, -2*w^2 - 2*w + 13],\ [137, 137, w^2 + 2*w - 10],\ [149, 149, 2*w^2 + 2*w - 19],\ [163, 163, w^2 - 2*w - 5],\ [173, 173, 3*w^2 - 20],\ [181, 181, 2*w^2 - w - 17],\ [191, 191, 2*w^2 - w - 16],\ [193, 193, 2*w^2 - 2*w - 11],\ [197, 197, -7*w^2 - 13*w + 23],\ [199, 199, -2*w^2 - 5*w + 4],\ [199, 199, -w^2 + w + 13],\ [199, 199, -w^2 - 4*w - 2],\ [211, 211, w^2 + 3*w - 14],\ [223, 223, 3*w - 10],\ [227, 227, 2*w^2 + w - 8],\ [227, 227, -2*w^2 - 5*w + 5],\ [227, 227, 5*w^2 + 7*w - 20],\ [229, 229, w^2 + w - 13],\ [233, 233, -2*w^2 - 5*w + 1],\ [233, 233, 3*w^2 + 3*w - 14],\ [233, 233, 3*w^2 + 2*w - 17],\ [241, 241, 3*w^2 + w - 19],\ [251, 251, 2*w^2 + w - 20],\ [257, 257, 3*w + 7],\ [269, 269, 5*w^2 + 4*w - 29],\ [271, 271, -2*w^2 + 3*w + 4],\ [277, 277, 5*w^2 + 8*w - 20],\ [281, 281, w^2 - 2*w - 7],\ [283, 283, -3*w^2 + 19],\ [293, 293, -2*w^2 + 7*w - 2],\ [307, 307, 3*w^2 + 3*w - 13],\ [311, 311, -3*w - 1],\ [311, 311, -3*w^2 + 7*w + 2],\ [311, 311, 5*w^2 + 6*w - 25],\ [313, 313, 3*w^2 + 2*w - 23],\ [331, 331, 2*w^2 + 4*w - 11],\ [337, 337, -4*w^2 - 4*w + 23],\ [337, 337, 6*w^2 + 3*w - 40],\ [337, 337, -3*w - 10],\ [343, 7, -7],\ [347, 347, 3*w^2 + 4*w - 16],\ [349, 349, w^2 + 5*w + 5],\ [349, 349, 2*w^2 - w - 7],\ [349, 349, 5*w - 11],\ [353, 353, 2*w^2 + 3*w - 13],\ [353, 353, w^2 - 2*w - 10],\ [353, 353, 2*w^2 - 2*w - 5],\ [359, 359, w^2 - 4*w - 1],\ [359, 359, 2*w^2 - w - 5],\ [359, 359, -5*w^2 - 3*w + 34],\ [361, 19, 4*w^2 + 5*w - 16],\ [367, 367, -3*w - 2],\ [383, 383, -5*w^2 - 5*w + 28],\ [383, 383, w^2 + w - 14],\ [383, 383, 3*w^2 - w - 17],\ [389, 389, 6*w^2 + 9*w - 25],\ [397, 397, -7*w^2 - 10*w + 28],\ [401, 401, -w^2 - w - 2],\ [419, 419, 3*w - 11],\ [419, 419, -3*w - 4],\ [421, 421, 3*w^2 + w - 28],\ [431, 431, -2*w^2 + 6*w + 1],\ [433, 433, 4*w - 13],\ [449, 449, -w^2 - 4*w - 5],\ [449, 449, w^2 + 4*w - 10],\ [449, 449, w^2 + 4*w - 16],\ [463, 463, 7*w^2 + 12*w - 26],\ [467, 467, -5*w^2 - 9*w + 13],\ [479, 479, w^2 - 14],\ [487, 487, w^2 - 3*w - 5],\ [499, 499, 4*w^2 + 4*w - 19],\ [499, 499, -5*w^2 - 3*w + 31],\ [499, 499, -3*w^2 - 6*w + 5],\ [503, 503, -w - 8],\ [521, 521, 4*w^2 + w - 26],\ [523, 523, w^2 + 2*w - 16],\ [529, 23, w^2 + 4*w - 11],\ [547, 547, 5*w^2 + 6*w - 22],\ [563, 563, 2*w^2 + 3*w - 16],\ [577, 577, 3*w^2 + w - 16],\ [593, 593, 5*w^2 - w - 37],\ [593, 593, 3*w^2 + 3*w - 28],\ [593, 593, 7*w^2 + 11*w - 28],\ [599, 599, 2*w^2 + 2*w - 23],\ [601, 601, w^2 + 4*w - 14],\ [613, 613, -6*w^2 - 7*w + 28],\ [617, 617, -6*w + 13],\ [619, 619, -6*w + 11],\ [631, 631, -6*w^2 - 6*w + 31],\ [643, 643, 2*w^2 + 3*w - 25],\ [659, 659, -3*w - 11],\ [661, 661, 3*w^2 - 16],\ [683, 683, 5*w + 13],\ [691, 691, w^2 - 5*w + 10],\ [709, 709, w^2 + 6*w - 11],\ [719, 719, 3*w^2 + 3*w - 22],\ [727, 727, -w^2 + 3*w - 7],\ [733, 733, -4*w^2 - 4*w + 13],\ [743, 743, 2*w^2 + 2*w - 1],\ [751, 751, 5*w^2 + 5*w - 29],\ [757, 757, 3*w^2 - 2*w - 13],\ [761, 761, 4*w^2 + 4*w - 17],\ [769, 769, 6*w^2 + 9*w - 26],\ [773, 773, 2*w^2 + 3*w - 1],\ [773, 773, 2*w^2 + 5*w - 13],\ [773, 773, 11*w^2 + 16*w - 44],\ [787, 787, 3*w^2 - 3*w - 17],\ [787, 787, w^2 - 3*w - 8],\ [787, 787, -3*w^2 + 3*w + 32],\ [809, 809, -w^2 + w - 5],\ [809, 809, -2*w^2 - 7*w + 8],\ [809, 809, 2*w - 11],\ [811, 811, 3*w^2 + 3*w - 26],\ [821, 821, -3*w^2 + 4*w + 8],\ [823, 823, 4*w^2 + 3*w - 29],\ [827, 827, -w^2 - 5*w - 8],\ [829, 829, w - 10],\ [839, 839, 3*w^2 + 6*w - 4],\ [841, 29, 3*w^2 + w - 13],\ [857, 857, 7*w^2 + 10*w - 26],\ [857, 857, w^2 - 4*w - 4],\ [857, 857, 3*w^2 + 4*w - 31],\ [859, 859, -w^2 - 5*w - 2],\ [859, 859, -w^2 - w - 4],\ [859, 859, 3*w^2 - 4*w - 14],\ [863, 863, 5*w^2 + 2*w - 32],\ [881, 881, -7*w + 16],\ [887, 887, 4*w^2 + 3*w - 20],\ [907, 907, w^2 - 3*w - 11],\ [907, 907, 3*w^2 - 3*w - 10],\ [907, 907, 3*w^2 + 5*w - 17],\ [911, 911, w^2 + 5*w - 13],\ [929, 929, w^2 + 6*w + 7],\ [937, 937, 7*w^2 + 10*w - 25],\ [953, 953, 7*w^2 + 10*w - 31],\ [961, 31, 2*w^2 + 5*w - 14],\ [977, 977, 2*w^2 + w - 23],\ [983, 983, 3*w^2 + 6*w - 16],\ [991, 991, -4*w - 5],\ [997, 997, 3*w - 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -1, 0, -3, 2, 4, 4, 4, 0, 4, 0, 4, 6, 0, -12, 2, 4, 6, 0, 0, -6, 6, -6, 4, 0, 4, -16, 0, 0, 0, -4, 0, -10, 24, 14, -6, 8, -16, -16, 4, 8, 0, 12, -24, -10, -6, 0, 24, 4, 12, -18, 24, -20, 4, 6, 4, 6, 4, 0, 24, -24, -20, 28, 4, 4, 2, 8, 24, 2, -20, 28, 24, 30, -24, -24, -24, -24, -20, 32, -24, 0, -24, -24, -20, -30, 12, 12, -10, 24, 2, -30, 24, 0, 4, 12, 24, -16, -20, 28, -4, 0, 0, -4, -20, -20, 24, 28, 18, 24, -48, 24, 28, -20, -48, 28, 4, -4, 12, -20, -36, 20, 4, 48, -16, 4, -24, 4, -44, 0, -20, 6, 24, 48, -28, -4, -4, 6, -6, 6, 28, 24, 28, -12, 14, 0, 4, 48, -54, -24, -28, -4, 20, 24, 0, 0, -28, 52, -44, 48, 18, 28, -24, 28, 18, 24, -16, -22] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, -w + 3])] = -1 AL_eigenvalues[ZF.ideal([3, 3, w - 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]