/* 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, -1, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([6, 6, -w^2 + 3]) primes_array = [ [2, 2, -w^2 + w + 4],\ [3, 3, -w^2 + w + 3],\ [5, 5, w^2 - 4],\ [8, 2, w^3 - w^2 - 4*w + 5],\ [17, 17, -w^2 + w + 5],\ [27, 3, -w^3 + 4*w - 2],\ [29, 29, -w^2 + w + 1],\ [29, 29, -w^3 + 4*w + 2],\ [37, 37, -2*w^3 + 3*w^2 + 9*w - 13],\ [41, 41, w^3 - w^2 - 5*w + 2],\ [43, 43, -w^3 + w^2 + 3*w - 4],\ [61, 61, w^2 - 2*w - 2],\ [61, 61, 2*w^2 - w - 8],\ [67, 67, -4*w^3 + 5*w^2 + 18*w - 22],\ [73, 73, -w^2 - 2*w + 2],\ [79, 79, w^2 - 2*w - 4],\ [89, 89, w^2 + w - 5],\ [89, 89, 2*w^3 - 2*w^2 - 9*w + 8],\ [89, 89, w^3 - 5*w - 5],\ [89, 89, -w^3 + 2*w^2 + 4*w - 4],\ [97, 97, w^3 + w^2 - 5*w - 4],\ [101, 101, -2*w^3 + 2*w^2 + 8*w - 11],\ [103, 103, w^3 - 5*w + 1],\ [109, 109, 2*w - 1],\ [109, 109, -w^3 + 2*w^2 + 3*w - 7],\ [113, 113, 2*w^2 - 7],\ [125, 5, -w^3 + 3*w^2 + 3*w - 8],\ [127, 127, 2*w^3 - 4*w^2 - 11*w + 16],\ [131, 131, 3*w^2 + 2*w - 8],\ [131, 131, -2*w^3 + 4*w^2 + 8*w - 13],\ [137, 137, w^3 - 3*w^2 - 7*w + 10],\ [149, 149, -w^3 + 4*w - 4],\ [149, 149, w^2 - 2*w - 8],\ [157, 157, -w - 4],\ [163, 163, -w^3 + 2*w^2 + 6*w - 10],\ [167, 167, -w^3 + 2*w^2 + 5*w - 11],\ [167, 167, -3*w^2 - 2*w + 10],\ [167, 167, -w^2 - w + 7],\ [167, 167, 2*w^2 - 2*w - 5],\ [173, 173, -3*w^3 + 2*w^2 + 13*w - 11],\ [179, 179, w^3 - 3*w^2 - 5*w + 10],\ [191, 191, -2*w^3 - 3*w^2 + 10*w + 14],\ [191, 191, 3*w^2 + w - 7],\ [193, 193, w^2 - w + 1],\ [193, 193, -w^2 - w - 1],\ [227, 227, 4*w^3 - 4*w^2 - 17*w + 20],\ [227, 227, -3*w^3 + 4*w^2 + 13*w - 17],\ [229, 229, -w^3 + 6*w - 2],\ [233, 233, -3*w^3 + 3*w^2 + 13*w - 16],\ [241, 241, -w^2 + 2*w - 2],\ [263, 263, 2*w^3 - 5*w^2 - 12*w + 16],\ [263, 263, -3*w^3 + 4*w^2 + 13*w - 19],\ [269, 269, w^3 + 2*w^2 - 5*w - 7],\ [269, 269, -w^3 - 2*w^2 + w + 5],\ [281, 281, 2*w^3 - 2*w^2 - 8*w + 1],\ [281, 281, w^2 - 8],\ [289, 17, 2*w^3 - 10*w - 7],\ [307, 307, w^3 + 2*w^2 - 6*w - 8],\ [307, 307, -2*w^3 + 2*w^2 + 8*w - 7],\ [313, 313, 5*w^3 - 6*w^2 - 24*w + 28],\ [313, 313, 2*w^3 - 2*w^2 - 10*w + 5],\ [337, 337, w^3 - 2*w - 2],\ [347, 347, -w^3 + 4*w^2 + w - 13],\ [349, 349, -2*w^3 + w^2 + 9*w - 7],\ [353, 353, 2*w^3 + w^2 - 7*w + 1],\ [359, 359, -3*w^2 - 3*w + 5],\ [359, 359, 3*w^3 - 5*w^2 - 13*w + 16],\ [367, 367, 3*w^3 - 6*w^2 - 15*w + 23],\ [367, 367, -w^3 + 2*w^2 + 6*w - 4],\ [367, 367, -2*w^3 + 2*w^2 + 8*w - 5],\ [367, 367, 2*w^3 - 3*w^2 - 12*w + 16],\ [373, 373, -2*w^3 + 4*w^2 + 12*w - 17],\ [373, 373, 3*w^2 + 4*w - 8],\ [383, 383, -w^3 + 2*w^2 + 3*w - 13],\ [383, 383, 2*w^2 - 2*w - 11],\ [389, 389, 5*w^3 - 6*w^2 - 24*w + 26],\ [389, 389, -w^3 + 3*w - 5],\ [401, 401, w^3 + 2*w^2 - 4*w - 10],\ [401, 401, 2*w^3 - w^2 - 7*w + 5],\ [409, 409, -2*w^2 + 3*w + 10],\ [419, 419, w^2 - 3*w - 1],\ [419, 419, -w^3 + 5*w^2 + 9*w - 14],\ [421, 421, 2*w^3 - 8*w - 7],\ [431, 431, -3*w^2 + 16],\ [431, 431, -3*w^3 + 11*w - 7],\ [433, 433, 4*w^3 - 7*w^2 - 18*w + 26],\ [439, 439, 3*w - 2],\ [439, 439, -w^3 + w^2 + 5*w - 8],\ [443, 443, 2*w^3 - w^2 - 6*w + 4],\ [443, 443, w^2 + 3*w - 1],\ [449, 449, -2*w^3 + 5*w^2 + 7*w - 17],\ [457, 457, 4*w^3 - 6*w^2 - 19*w + 22],\ [479, 479, 3*w^2 - 3*w - 13],\ [479, 479, -4*w^3 + 8*w^2 + 22*w - 31],\ [479, 479, 3*w^3 - 7*w^2 - 17*w + 26],\ [479, 479, -6*w^3 + 7*w^2 + 28*w - 32],\ [487, 487, -2*w^3 + 4*w^2 + 7*w - 8],\ [491, 491, 3*w^2 - w - 11],\ [491, 491, 4*w^3 - 5*w^2 - 18*w + 20],\ [521, 521, -3*w^3 + 11*w - 5],\ [521, 521, 3*w^3 - 3*w^2 - 15*w + 14],\ [523, 523, -2*w^3 + 5*w^2 + 8*w - 14],\ [529, 23, -2*w^3 + 3*w^2 + 8*w - 14],\ [529, 23, 3*w^3 - 2*w^2 - 14*w + 4],\ [541, 541, -w^3 + 2*w^2 + 7*w - 11],\ [541, 541, -w^3 - w^2 + 5*w - 2],\ [547, 547, -3*w - 2],\ [547, 547, w^3 - 2*w^2 - 7*w + 7],\ [547, 547, w^3 - 4*w^2 - 8*w + 10],\ [547, 547, 2*w^3 - 3*w^2 - 7*w + 11],\ [563, 563, 2*w^3 - 4*w^2 - 12*w + 13],\ [563, 563, -w^3 + 4*w^2 + w - 7],\ [571, 571, -w^3 + 2*w^2 + 2*w - 8],\ [571, 571, 3*w^2 - 10],\ [577, 577, 2*w^3 + w^2 - 7*w - 5],\ [599, 599, 2*w^3 - 7*w + 2],\ [599, 599, -4*w^3 + 7*w^2 + 21*w - 29],\ [617, 617, -2*w^3 + w^2 + 11*w + 1],\ [631, 631, 3*w^2 + w - 13],\ [631, 631, 3*w^2 - 4*w - 10],\ [647, 647, 3*w^3 - 4*w^2 - 13*w + 11],\ [677, 677, -2*w^3 + 4*w^2 + 8*w - 17],\ [691, 691, -w^3 + 3*w^2 + 3*w - 14],\ [733, 733, -w^3 + 4*w^2 + 3*w - 11],\ [733, 733, 3*w^3 - w^2 - 15*w - 2],\ [733, 733, -w^3 + w^2 + 7*w - 2],\ [733, 733, 3*w^3 - 4*w^2 - 16*w + 16],\ [739, 739, -3*w^3 + w^2 + 11*w - 8],\ [743, 743, -3*w^3 + 2*w^2 + 12*w - 14],\ [751, 751, -2*w^3 + w^2 + 8*w - 2],\ [761, 761, -2*w^3 + 2*w^2 + 7*w - 10],\ [761, 761, 2*w^3 - 4*w^2 - 3*w + 8],\ [769, 769, -w^3 + w^2 + 7*w - 4],\ [769, 769, 2*w^3 + 2*w^2 - 8*w - 11],\ [787, 787, -2*w^3 + 3*w^2 + 6*w - 10],\ [787, 787, -2*w^2 - 3*w + 8],\ [797, 797, -2*w^3 + w^2 + 7*w - 1],\ [797, 797, -2*w^3 - 2*w^2 + 11*w + 10],\ [809, 809, -2*w^3 + 5*w^2 + 7*w - 19],\ [811, 811, 2*w^3 - 2*w^2 - 7*w - 2],\ [811, 811, 3*w^3 - 2*w^2 - 11*w - 1],\ [827, 827, 3*w^3 - 2*w^2 - 14*w + 10],\ [829, 829, 2*w^3 - 2*w^2 - 9*w + 2],\ [829, 829, 4*w^2 + 2*w - 11],\ [841, 29, 2*w^3 + w^2 - 6*w - 2],\ [863, 863, 2*w^3 - 8*w - 1],\ [883, 883, 3*w^3 - 4*w^2 - 15*w + 13],\ [887, 887, 3*w^3 - 2*w^2 - 12*w + 10],\ [907, 907, 2*w^3 - 3*w^2 - 9*w + 7],\ [911, 911, 2*w^3 + w^2 - 11*w - 5],\ [919, 919, -2*w^3 + 5*w - 8],\ [929, 929, -w^3 + 4*w^2 + 3*w - 13],\ [937, 937, w^3 - 5*w - 7],\ [937, 937, -2*w^3 + 3*w^2 + 10*w - 8],\ [971, 971, -2*w^3 + 4*w^2 + 11*w - 20],\ [971, 971, -4*w^3 + 4*w^2 + 19*w - 20],\ [977, 977, -4*w^3 + 6*w^2 + 19*w - 28],\ [983, 983, -4*w^2 - 4*w + 7],\ [991, 991, -5*w^3 + 8*w^2 + 26*w - 32],\ [991, 991, -6*w^3 + 6*w^2 + 26*w - 31],\ [997, 997, -3*w^3 + 8*w^2 + 18*w - 26]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -1, -3, -3, -3, 2, 3, -9, 1, -3, 10, -11, 1, 4, 11, -4, 15, 15, -9, -15, 1, -6, 14, 1, 10, -15, 3, 16, -6, 6, -21, -6, -9, -19, -2, 12, -24, -12, -6, 6, -6, -12, -6, -19, 2, 6, 18, -5, -18, -14, 6, 18, 18, 3, 21, -18, 25, -34, -8, -10, 7, -13, -18, 14, -15, -24, 30, 10, 2, 8, 22, -31, 11, -6, 18, -21, -15, 21, -27, 31, 12, 0, -11, 24, -30, -2, -28, -2, -12, 18, -30, -22, 0, 0, 36, -30, -38, -18, -18, -39, 9, -38, -13, -5, 35, -2, -32, -38, -28, 20, -42, -36, -10, -22, 10, 18, -6, -18, -20, 20, -48, -33, 32, 19, -13, -13, -5, -46, 12, 20, 6, 15, -14, -1, 22, -46, -27, 6, -3, 16, -34, -48, 13, 34, -38, 6, -10, 48, 26, 24, 2, -21, 17, -2, 0, 30, 39, 48, -16, 26, 55] 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^2 + w + 4])] = -1 AL_eigenvalues[ZF.ideal([3, 3, -w^2 + w + 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]