/* 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([10, -8, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([10, 10, w^2 + 2*w - 5]) primes_array = [ [2, 2, -w + 2],\ [2, 2, -w + 1],\ [5, 5, -w^2 - w + 5],\ [7, 7, w^2 + w - 9],\ [13, 13, -w^2 - w + 7],\ [19, 19, w^2 - w - 1],\ [25, 5, -w^2 + w + 3],\ [27, 3, 3],\ [31, 31, -w^2 + w + 11],\ [43, 43, -3*w^2 - w + 21],\ [47, 47, 2*w - 1],\ [49, 7, 4*w^2 + 2*w - 29],\ [61, 61, 2*w^2 + 2*w - 9],\ [71, 71, w^2 + w - 11],\ [71, 71, -w^2 - 3*w + 7],\ [71, 71, 2*w^2 + 2*w - 13],\ [79, 79, w^2 + 3*w - 1],\ [79, 79, w^2 + w - 1],\ [79, 79, -w^2 - 3*w - 1],\ [83, 83, w^2 - w - 7],\ [97, 97, 4*w^2 + 4*w - 23],\ [101, 101, -w^2 + w + 9],\ [101, 101, w^2 + 3*w - 3],\ [101, 101, 2*w - 7],\ [107, 107, 2*w^2 + 2*w - 17],\ [107, 107, 5*w^2 + 7*w - 21],\ [107, 107, w^2 - 3*w - 1],\ [109, 109, -2*w - 1],\ [109, 109, 4*w - 7],\ [109, 109, 4*w^2 + 2*w - 27],\ [113, 113, 2*w^2 - 11],\ [127, 127, -2*w^2 + 2*w + 7],\ [131, 131, -2*w - 3],\ [137, 137, 2*w + 7],\ [139, 139, -5*w^2 - 3*w + 33],\ [149, 149, -w^2 - 3*w + 13],\ [157, 157, w^2 - 5*w + 3],\ [163, 163, -4*w^2 + 33],\ [163, 163, 7*w^2 + 3*w - 53],\ [163, 163, -8*w^2 - 4*w + 57],\ [169, 13, w^2 + 3*w - 9],\ [173, 173, 3*w^2 + w - 19],\ [179, 179, 6*w^2 + 2*w - 43],\ [193, 193, -6*w + 7],\ [197, 197, -5*w^2 - w + 41],\ [197, 197, 4*w^2 + 4*w - 21],\ [197, 197, 3*w^2 + 3*w - 19],\ [199, 199, 2*w^2 - 9],\ [211, 211, w^2 + 3*w - 11],\ [223, 223, w^2 + 5*w - 7],\ [223, 223, 5*w^2 + 5*w - 27],\ [227, 227, -2*w^2 + 2*w + 3],\ [229, 229, 2*w^2 - 7],\ [233, 233, -4*w - 11],\ [239, 239, 4*w^2 + 6*w - 19],\ [251, 251, 5*w^2 + 5*w - 29],\ [269, 269, w^2 + w - 13],\ [277, 277, -w^2 - w - 1],\ [283, 283, 2*w^2 + 4*w - 3],\ [293, 293, -4*w^2 + 31],\ [313, 313, 3*w^2 - w - 27],\ [337, 337, 2*w^2 + 2*w - 21],\ [347, 347, -2*w^2 - 6*w + 13],\ [353, 353, -5*w^2 - 3*w + 37],\ [353, 353, 2*w^2 + 4*w - 13],\ [353, 353, -w^2 + w - 3],\ [359, 359, 2*w - 9],\ [361, 19, -7*w^2 - 3*w + 49],\ [367, 367, w^2 - 5*w + 9],\ [373, 373, 3*w^2 + w - 27],\ [379, 379, -w^2 - 5*w - 7],\ [397, 397, -w^2 - 5*w + 11],\ [401, 401, 6*w^2 + 4*w - 41],\ [401, 401, -9*w^2 - 3*w + 71],\ [401, 401, 6*w - 13],\ [409, 409, 2*w^2 - 2*w + 1],\ [419, 419, 4*w^2 + 4*w - 19],\ [421, 421, -w^2 - 3*w - 3],\ [433, 433, 2*w^2 + 6*w - 1],\ [433, 433, 9*w^2 + 5*w - 63],\ [433, 433, 3*w^2 + 3*w - 23],\ [443, 443, -3*w^2 - 7*w + 7],\ [449, 449, -3*w^2 - 3*w + 7],\ [457, 457, -2*w^2 - 6*w + 9],\ [463, 463, -3*w^2 - w + 9],\ [479, 479, -w^2 - 3*w + 17],\ [487, 487, -w^2 + 5*w - 1],\ [499, 499, -14*w^2 - 4*w + 109],\ [509, 509, 4*w - 1],\ [509, 509, -5*w^2 - w + 33],\ [509, 509, -3*w^2 - 5*w + 17],\ [521, 521, -15*w^2 - 5*w + 111],\ [523, 523, -2*w^2 + 6*w - 7],\ [523, 523, 2*w^2 - 21],\ [523, 523, 2*w + 9],\ [541, 541, 5*w^2 + 3*w - 31],\ [547, 547, -w^2 - 5*w + 17],\ [557, 557, -3*w^2 + w + 23],\ [563, 563, -4*w^2 - 8*w + 9],\ [563, 563, 2*w^2 - 2*w - 13],\ [563, 563, -2*w^2 + 6*w + 1],\ [569, 569, -4*w - 13],\ [593, 593, 8*w - 9],\ [599, 599, w^2 + 5*w - 13],\ [601, 601, w^2 + 7*w - 13],\ [613, 613, 3*w^2 + w - 11],\ [641, 641, 4*w^2 + 2*w - 23],\ [643, 643, -w^2 - w - 3],\ [647, 647, -3*w^2 - 7*w + 17],\ [653, 653, 3*w^2 - w - 13],\ [659, 659, w^2 + 7*w - 9],\ [661, 661, 2*w^2 + 4*w - 17],\ [677, 677, -6*w^2 + 49],\ [677, 677, -11*w^2 - 5*w + 81],\ [677, 677, -14*w^2 - 6*w + 103],\ [683, 683, 2*w^2 + 4*w - 19],\ [691, 691, w^2 - 3*w + 7],\ [691, 691, -8*w + 13],\ [691, 691, 3*w^2 - 5*w - 3],\ [709, 709, 4*w^2 + 4*w - 27],\ [719, 719, -w^2 - 7*w - 11],\ [727, 727, -13*w^2 - 3*w + 99],\ [739, 739, -5*w^2 - w + 43],\ [739, 739, 4*w + 9],\ [739, 739, -w^2 + 3*w + 19],\ [743, 743, 2*w^2 - 4*w - 7],\ [751, 751, 7*w^2 + 5*w - 47],\ [757, 757, -8*w^2 + 69],\ [761, 761, w^2 - 3*w - 7],\ [773, 773, -2*w^2 - 4*w + 1],\ [809, 809, -10*w^2 - 4*w + 71],\ [811, 811, w^2 + 5*w - 3],\ [811, 811, -8*w^2 - 10*w + 37],\ [811, 811, 6*w^2 + 6*w - 31],\ [823, 823, 2*w^2 - 2*w - 17],\ [823, 823, 3*w^2 - w - 11],\ [823, 823, -3*w^2 - 5*w + 19],\ [829, 829, 7*w^2 + 5*w - 43],\ [853, 853, -3*w^2 + 3*w + 7],\ [857, 857, 3*w^2 + 7*w - 3],\ [857, 857, 4*w^2 - 2*w - 19],\ [857, 857, 3*w^2 - w - 9],\ [859, 859, 2*w^2 + 2*w - 23],\ [859, 859, -10*w^2 - 6*w + 69],\ [859, 859, -3*w^2 - 5*w + 31],\ [877, 877, -10*w^2 - 2*w + 81],\ [883, 883, 7*w^2 + 7*w - 41],\ [883, 883, 3*w^2 + w - 29],\ [883, 883, 8*w^2 + 6*w - 49],\ [887, 887, 16*w^2 + 6*w - 117],\ [907, 907, 5*w^2 + 5*w - 23],\ [911, 911, w^2 - 3*w - 13],\ [919, 919, 5*w^2 + 5*w - 19],\ [919, 919, 3*w^2 + 3*w - 31],\ [919, 919, 4*w^2 + 2*w - 21],\ [937, 937, w^2 - 5*w - 1],\ [947, 947, -7*w^2 - 3*w + 47],\ [953, 953, 7*w^2 + 7*w - 37],\ [961, 31, -5*w^2 + w + 47],\ [967, 967, 4*w^2 + 4*w - 33],\ [967, 967, -5*w^2 - w + 31],\ [967, 967, -6*w^2 + 47],\ [977, 977, -7*w^2 - w + 59],\ [983, 983, -w^2 - 5*w - 1],\ [983, 983, 8*w - 17],\ [983, 983, 5*w^2 + 3*w - 29],\ [991, 991, 6*w^2 + 8*w - 31],\ [991, 991, -11*w^2 - 3*w + 79],\ [991, 991, w^2 + 7*w + 13],\ [997, 997, -4*w - 7],\ [997, 997, w^2 - 3*w - 11],\ [997, 997, -w^2 + 5*w - 11]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, 1, 1, -2, -6, 0, -4, -2, -8, 4, -2, -10, 2, 12, 12, 2, 0, 10, -10, -16, -2, 2, 2, -18, -12, -12, -12, -10, 0, 10, -6, 8, 12, -12, -10, -10, 8, 4, 4, -6, -10, -6, -20, -6, -2, 8, 18, 0, 12, 4, 24, -12, -10, -6, 20, 12, 30, 8, -26, 24, -16, -2, 8, 14, -26, -26, -20, -38, -22, 14, 20, 8, -18, -8, -8, 30, -30, 2, -36, 34, -6, 4, 30, 8, -16, 0, -12, -20, -40, -30, 30, -38, 44, 4, -36, -18, 28, 18, 24, 4, 24, -30, 14, 40, 22, -26, 2, 4, 48, -36, 40, -8, -12, 38, 18, 24, 12, 42, -28, -40, 0, -32, -40, -30, -50, 24, 32, -42, -38, 34, 10, -38, -28, -8, -16, 44, 4, -20, 4, 18, -12, -42, 40, -20, -10, 18, -46, 24, -16, 48, 38, 22, 40, -10, 50, -22, 28, 54, -38, -32, 48, 48, 38, -16, 4, 24, -8, -28, 12, 38, -2, 28] 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([5, 5, -w^2 - w + 5])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]