/* 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([1, -3, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([26, 26, -w - 3]) primes_array = [ [2, 2, w - 1],\ [5, 5, -w^2 + w + 1],\ [13, 13, -w^2 + 2*w + 2],\ [17, 17, 2*w + 1],\ [19, 19, -w^2 + 2*w + 4],\ [23, 23, -w^2 - w + 3],\ [25, 5, -2*w^2 + w + 4],\ [27, 3, 3],\ [29, 29, w^2 - 3*w - 1],\ [31, 31, 2*w^2 - 2*w - 3],\ [37, 37, w^2 + w - 5],\ [37, 37, w - 4],\ [43, 43, 2*w^2 - w - 2],\ [59, 59, 2*w^2 - 3*w - 6],\ [61, 61, -3*w^2 + 4*w + 4],\ [67, 67, -w - 4],\ [67, 67, -3*w^2 + 8],\ [67, 67, w^2 - 3*w - 3],\ [79, 79, w^2 + 2*w - 4],\ [89, 89, 3*w^2 - 3*w - 5],\ [97, 97, -3*w^2 + 4],\ [103, 103, -w^2 + w - 3],\ [107, 107, 3*w^2 - w - 5],\ [107, 107, w^2 - w - 7],\ [107, 107, -2*w - 5],\ [109, 109, w^2 + 2*w - 6],\ [113, 113, -2*w^2 + 5*w + 2],\ [131, 131, -5*w^2 + 3*w + 13],\ [137, 137, 2*w^2 - 4*w - 5],\ [137, 137, 2*w^2 + w - 8],\ [137, 137, 3*w^2 - 10],\ [139, 139, -w^2 + 2*w - 4],\ [139, 139, 4*w^2 - 2*w - 9],\ [139, 139, 3*w^2 - 2*w - 4],\ [151, 151, w^2 - 8],\ [151, 151, 4*w - 5],\ [151, 151, w^2 + w - 9],\ [163, 163, w - 6],\ [167, 167, 2*w^2 - 4*w - 7],\ [169, 13, w^2 - 4*w - 4],\ [179, 179, w^2 + 3*w - 5],\ [191, 191, 4*w^2 - 4*w - 7],\ [193, 193, 4*w^2 - 3*w - 8],\ [199, 199, w^2 + 3*w - 9],\ [227, 227, 2*w^2 - 5*w - 4],\ [233, 233, -w - 6],\ [233, 233, w^2 + 3*w - 7],\ [233, 233, 2*w^2 + 2*w - 7],\ [239, 239, 3*w^2 + w - 9],\ [241, 241, -5*w^2 + w + 15],\ [251, 251, 4*w^2 - 5*w - 4],\ [257, 257, 4*w^2 - 2*w - 7],\ [269, 269, 4*w^2 - w - 6],\ [269, 269, w^2 - 5*w - 3],\ [269, 269, 2*w^2 + 2*w - 11],\ [277, 277, 4*w^2 + w - 10],\ [281, 281, -w^2 + 7*w - 5],\ [283, 283, -3*w^2 + 5*w + 11],\ [289, 17, 4*w^2 - 6*w - 9],\ [293, 293, 3*w^2 - 5*w - 9],\ [293, 293, 4*w^2 - 4*w - 5],\ [293, 293, 2*w^2 + 3*w - 6],\ [311, 311, 4*w^2 - 13],\ [313, 313, -w^2 + w - 5],\ [317, 317, w^2 - w - 9],\ [317, 317, 2*w^2 - 5*w - 6],\ [317, 317, 2*w^2 - 6*w - 3],\ [331, 331, w^2 - 5*w - 5],\ [343, 7, -7],\ [347, 347, -5*w^2 + 7*w + 11],\ [349, 349, -2*w - 7],\ [349, 349, 4*w^2 - 15],\ [349, 349, 6*w - 5],\ [353, 353, 2*w^2 - w - 12],\ [361, 19, 4*w^2 + 2*w - 9],\ [367, 367, 5*w^2 - 2*w - 10],\ [367, 367, 2*w^2 - 3*w - 12],\ [367, 367, -5*w^2 + 6*w + 16],\ [383, 383, -7*w^2 + 4*w + 18],\ [389, 389, -w^2 + 2*w - 6],\ [401, 401, 6*w^2 - 3*w - 14],\ [409, 409, w^2 - 7*w - 1],\ [421, 421, w^2 + 4*w - 8],\ [431, 431, 4*w^2 - 6*w - 11],\ [439, 439, 2*w^2 + 3*w - 8],\ [449, 449, w^2 + w - 11],\ [457, 457, -4*w^2 - 4*w + 7],\ [461, 461, 3*w^2 + 2*w - 16],\ [463, 463, 5*w^2 - 6*w - 6],\ [467, 467, 2*w - 9],\ [479, 479, 4*w^2 + w - 12],\ [487, 487, 5*w^2 - 3*w - 9],\ [491, 491, w^2 - 2*w - 10],\ [491, 491, 3*w^2 + 2*w - 10],\ [491, 491, w^2 - 6*w - 8],\ [499, 499, 3*w^2 - 7*w - 5],\ [503, 503, w^2 - 6*w - 4],\ [523, 523, 5*w^2 - 5*w - 7],\ [529, 23, 2*w^2 + 3*w - 10],\ [541, 541, 5*w^2 - 2*w - 8],\ [547, 547, 6*w^2 - 4*w - 13],\ [557, 557, 5*w^2 - 6*w - 4],\ [563, 563, 3*w^2 - 6*w - 10],\ [569, 569, 5*w^2 - 7*w - 13],\ [577, 577, 2*w^2 - 6*w - 7],\ [587, 587, 5*w^2 - 8*w - 10],\ [601, 601, 6*w^2 - 5*w - 12],\ [601, 601, -7*w - 2],\ [601, 601, 5*w^2 - 3*w - 3],\ [607, 607, 3*w^2 + 2*w - 14],\ [631, 631, 4*w^2 + 2*w - 11],\ [643, 643, 5*w^2 - 2*w - 6],\ [647, 647, 3*w^2 - 8*w - 4],\ [653, 653, 5*w^2 - 4*w - 6],\ [661, 661, w^2 - 3*w - 11],\ [683, 683, 5*w^2 - 3*w - 5],\ [691, 691, -12*w^2 + 7*w + 34],\ [691, 691, -w^2 + w - 7],\ [691, 691, -w^2 - 5*w + 11],\ [701, 701, -5*w^2 + 7*w + 17],\ [709, 709, 5*w^2 - 10*w - 6],\ [727, 727, 6*w^2 - w - 10],\ [757, 757, -7*w^2 + 8*w + 12],\ [769, 769, 7*w - 8],\ [797, 797, -2*w^2 + 4*w - 7],\ [809, 809, 6*w^2 - 4*w - 11],\ [823, 823, 2*w^2 - 7*w - 6],\ [823, 823, -3*w^2 - 4],\ [823, 823, -w^2 + 2*w - 8],\ [827, 827, 3*w^2 - 7*w - 13],\ [829, 829, -5*w^2 + 4*w + 22],\ [839, 839, 5*w^2 + w - 15],\ [839, 839, -9*w^2 + 5*w + 23],\ [839, 839, 7*w^2 - 3*w - 15],\ [841, 29, 4*w^2 - 7*w - 14],\ [853, 853, 3*w^2 + 3*w - 17],\ [857, 857, 2*w^2 + 4*w - 13],\ [859, 859, 6*w^2 - 5*w - 10],\ [863, 863, w^2 + 6*w - 8],\ [863, 863, 5*w^2 - 9*w - 9],\ [863, 863, -2*w^2 + 5*w - 8],\ [877, 877, 2*w^2 - 15],\ [877, 877, 4*w^2 + 2*w - 13],\ [877, 877, 7*w^2 - 5*w - 15],\ [881, 881, 7*w^2 - 2*w - 14],\ [881, 881, 5*w^2 - 8*w - 12],\ [881, 881, 7*w^2 - 7*w - 13],\ [883, 883, w^2 - 7*w - 7],\ [907, 907, 4*w^2 - 9*w - 6],\ [911, 911, -10*w^2 + 5*w + 26],\ [919, 919, -w^2 + 3*w - 9],\ [929, 929, 6*w^2 - w - 8],\ [929, 929, 2*w^2 - 7*w - 8],\ [929, 929, -7*w^2 + 11*w + 1],\ [941, 941, 6*w^2 - 7*w - 6],\ [941, 941, 3*w^2 - 8*w - 6],\ [941, 941, 6*w^2 + w - 16],\ [947, 947, w^2 + w - 13],\ [961, 31, 6*w^2 - 2*w - 9],\ [967, 967, -w^2 + 4*w - 10],\ [971, 971, 4*w^2 - 8*w - 9],\ [971, 971, w^2 + 2*w - 14],\ [971, 971, 4*w^2 - 5*w - 20],\ [977, 977, 3*w^2 + 3*w - 13],\ [991, 991, -9*w^2 + 10*w + 32],\ [997, 997, w^2 - 2*w - 12]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 3, 1, 0, 5, -3, -7, -5, -9, 2, -7, -7, -1, 9, -10, 8, -10, -4, 5, 12, 14, 8, 18, 18, -15, 2, -9, 9, 18, 0, 0, -13, 20, 2, 20, 8, -19, 14, 3, 17, -24, 3, -10, 2, 0, -24, -24, -6, 9, -4, -12, 15, 0, -6, -9, 17, 24, -7, -22, 12, 24, -18, 18, 14, 24, -33, -24, 26, -16, -24, 26, -10, -4, -15, 14, 11, -19, -10, -30, 21, -30, 2, -10, 0, -28, 18, 14, 12, 23, 6, -24, -22, 42, 30, 0, -7, 12, 20, 32, -7, -28, -6, 21, 24, 32, -12, -4, -19, 20, -13, 11, 38, -33, -27, -40, 24, -22, 44, 26, -33, 8, 32, 26, -10, -42, 42, 14, 56, 17, 3, 29, -24, -27, -21, 26, -25, -27, 41, -9, -21, 15, -13, -4, -22, 15, -30, -12, -22, -37, -24, 11, -21, -18, -27, -45, 48, 48, -27, -34, 20, -24, 48, -36, -3, 20, 17] 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])] = 1 AL_eigenvalues[ZF.ideal([13, 13, -w^2 + 2*w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]