/* 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, 2, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([3, 3, w + 1]) primes_array = [ [2, 2, -w],\ [3, 3, w + 1],\ [4, 2, -w^2 - w + 1],\ [13, 13, -w^2 + 3],\ [17, 17, -w + 3],\ [27, 3, w^3 - 2*w^2 - 3*w + 5],\ [31, 31, -w^2 - 2*w + 1],\ [41, 41, -w^2 + 5],\ [43, 43, w^3 - w^2 - 5*w - 1],\ [43, 43, w^3 - w^2 - 3*w + 1],\ [59, 59, -w - 3],\ [59, 59, -2*w^3 + 2*w^2 + 9*w - 5],\ [59, 59, -w^3 - 3*w^2 - w + 3],\ [59, 59, w^3 - 7*w + 1],\ [61, 61, -w^3 + w^2 + 2*w + 5],\ [61, 61, -w^3 - w^2 + 4*w + 3],\ [67, 67, 4*w^3 - 4*w^2 - 18*w + 7],\ [73, 73, -2*w^3 + 6*w - 3],\ [73, 73, -2*w + 3],\ [97, 97, w^3 - 2*w^2 - 5*w + 3],\ [101, 101, w^3 + w^2 - 5*w - 7],\ [101, 101, -w^3 - w^2 + 4*w + 5],\ [103, 103, 2*w^3 - 8*w - 1],\ [103, 103, w^2 - 2*w - 7],\ [109, 109, -w^3 + 2*w^2 + 3*w - 7],\ [113, 113, -w^3 + w^2 + 6*w - 3],\ [127, 127, -w^3 + w^2 + 6*w - 1],\ [131, 131, -2*w^3 + 3*w^2 + 10*w - 11],\ [137, 137, w^3 + w^2 - 6*w - 5],\ [139, 139, -3*w^3 + 2*w^2 + 15*w - 1],\ [149, 149, w^3 - 3*w^2 - 4*w + 11],\ [149, 149, -w^3 + 5*w - 1],\ [157, 157, -2*w^3 + 3*w^2 + 6*w - 1],\ [163, 163, 2*w^2 - 3],\ [163, 163, -2*w^3 + 2*w^2 + 7*w - 5],\ [167, 167, -2*w^3 + 2*w^2 + 8*w - 3],\ [167, 167, -2*w^2 + 2*w + 9],\ [173, 173, 2*w^3 - w^2 - 8*w + 3],\ [173, 173, 2*w^3 - 3*w^2 - 6*w + 3],\ [181, 181, 2*w^3 - 3*w^2 - 8*w + 5],\ [191, 191, -2*w^3 + w^2 + 10*w - 1],\ [193, 193, -w^3 + 3*w^2 + 2*w - 7],\ [193, 193, w^3 - 3*w - 3],\ [193, 193, 2*w^2 - 2*w - 3],\ [193, 193, w^3 - 7*w - 1],\ [197, 197, w^2 - 2*w - 5],\ [211, 211, w^2 - 4*w - 1],\ [229, 229, -w^3 + w^2 + 6*w - 7],\ [229, 229, -4*w^3 + 6*w^2 + 16*w - 13],\ [233, 233, 3*w^2 + 2*w - 5],\ [233, 233, 2*w^3 - 2*w^2 - 11*w + 7],\ [239, 239, -w^3 + w^2 + 7*w + 1],\ [241, 241, w^3 - 3*w^2 - 2*w + 9],\ [241, 241, w^3 + w^2 - 9*w - 5],\ [251, 251, 2*w^3 - 6*w + 1],\ [271, 271, 2*w^3 - w^2 - 8*w - 1],\ [271, 271, -2*w^2 + w + 7],\ [281, 281, 2*w^3 + 2*w^2 - 5*w - 1],\ [293, 293, w^3 + w^2 - 5*w - 1],\ [293, 293, -3*w + 7],\ [307, 307, -w^3 - 2*w^2 + 3*w + 5],\ [311, 311, -w^3 + 3*w^2 + 4*w - 7],\ [313, 313, 2*w^2 - 2*w - 5],\ [317, 317, -2*w^3 + 4*w^2 + 7*w - 13],\ [317, 317, -2*w^3 + 3*w^2 + 8*w - 11],\ [337, 337, 3*w^3 + 2*w^2 - 7*w + 1],\ [347, 347, 2*w^3 - 2*w^2 - 11*w + 1],\ [349, 349, -5*w^3 + 6*w^2 + 23*w - 13],\ [359, 359, 2*w^3 - 2*w^2 - 12*w + 9],\ [359, 359, -2*w^3 + 8*w + 5],\ [367, 367, -4*w^3 + 4*w^2 + 19*w - 5],\ [367, 367, 2*w^3 + w^2 - 10*w - 7],\ [383, 383, 2*w^3 - 2*w^2 - 7*w + 1],\ [389, 389, 2*w^2 - w - 5],\ [397, 397, 3*w^3 - 4*w^2 - 11*w + 9],\ [397, 397, 3*w^3 - 3*w^2 - 12*w + 7],\ [397, 397, 2*w^3 - 4*w^2 - 8*w + 15],\ [397, 397, -w^3 + 3*w^2 + w - 7],\ [409, 409, -w^3 - w^2 + 9*w - 1],\ [419, 419, 2*w^2 - 3*w - 7],\ [419, 419, 4*w^3 - 3*w^2 - 18*w + 3],\ [431, 431, -3*w^3 + w^2 + 17*w - 1],\ [431, 431, 3*w^3 - w^2 - 16*w - 1],\ [433, 433, -2*w^3 + 5*w^2 + 8*w - 19],\ [443, 443, 3*w - 5],\ [449, 449, -2*w^3 + 2*w^2 + 9*w - 9],\ [449, 449, -5*w^3 + 8*w^2 + 19*w - 17],\ [457, 457, -3*w^3 + 3*w^2 + 13*w - 9],\ [457, 457, -3*w^3 + 2*w^2 + 13*w + 1],\ [457, 457, -2*w^3 + w^2 + 8*w + 7],\ [457, 457, 3*w^3 - 3*w^2 - 15*w + 7],\ [461, 461, -2*w^3 + 2*w^2 + 9*w + 1],\ [479, 479, -w^3 + w^2 + 7*w - 9],\ [487, 487, -w^3 - w^2 + w - 3],\ [499, 499, -2*w^3 + 7*w - 3],\ [499, 499, -5*w^3 + 7*w^2 + 20*w - 15],\ [541, 541, -3*w^3 + 4*w^2 + 13*w - 7],\ [547, 547, -w^3 - w^2 + 3*w + 5],\ [557, 557, 4*w - 1],\ [563, 563, 2*w^3 - w^2 - 6*w - 1],\ [571, 571, w^3 - w^2 - w - 3],\ [587, 587, -2*w^3 + 2*w^2 + 10*w + 1],\ [593, 593, 2*w^3 - 2*w^2 - 6*w + 3],\ [613, 613, -5*w^3 + 5*w^2 + 23*w - 7],\ [613, 613, -w^3 + w^2 + 5*w - 7],\ [617, 617, -w - 5],\ [619, 619, -3*w^3 + 4*w^2 + 11*w - 7],\ [625, 5, -5],\ [643, 643, -3*w^3 + 3*w^2 + 14*w - 9],\ [643, 643, -3*w^2 - 4*w + 1],\ [653, 653, -w^3 + w^2 + 9*w + 3],\ [653, 653, -4*w^2 + 6*w + 11],\ [659, 659, -w^2 - 4*w + 1],\ [661, 661, -3*w^3 + 3*w^2 + 15*w - 5],\ [661, 661, w^3 + w^2 - 7*w - 11],\ [673, 673, 2*w^3 - 3*w^2 - 12*w + 1],\ [673, 673, -2*w^3 + w^2 + 10*w - 3],\ [683, 683, -w^3 - 2*w^2 + 5*w + 11],\ [691, 691, 4*w^3 - 3*w^2 - 18*w + 5],\ [709, 709, w^3 - 3*w - 7],\ [719, 719, 2*w^3 - 8*w + 1],\ [727, 727, -3*w^3 + 6*w^2 + 13*w - 19],\ [733, 733, w^3 - w^2 + 3],\ [739, 739, -w^3 + w^2 + 3*w - 7],\ [751, 751, -w^2 - 3],\ [773, 773, 2*w^3 - 2*w^2 - 11*w + 3],\ [787, 787, w^3 - w^2 - 3*w - 5],\ [797, 797, -2*w^3 + 2*w^2 + 5*w - 1],\ [797, 797, -7*w^3 + 8*w^2 + 31*w - 15],\ [809, 809, 4*w^3 - 6*w^2 - 17*w + 13],\ [809, 809, 3*w^2 - 4*w - 5],\ [811, 811, 2*w^2 + 4*w + 3],\ [811, 811, -3*w^3 + 3*w^2 + 12*w - 5],\ [821, 821, 2*w^3 - 10*w - 1],\ [821, 821, 6*w^3 - 10*w^2 - 24*w + 29],\ [823, 823, -5*w^3 + 3*w^2 + 24*w - 1],\ [823, 823, w^3 + w^2 + w + 3],\ [827, 827, -4*w^3 + 3*w^2 + 16*w - 7],\ [829, 829, 2*w^3 - 4*w^2 - 6*w + 11],\ [841, 29, w^3 - 3*w^2 - 5*w + 3],\ [841, 29, -3*w^3 + 3*w^2 + 13*w - 1],\ [857, 857, -4*w^3 + 6*w^2 + 13*w - 7],\ [857, 857, -3*w^3 + w^2 + 15*w + 1],\ [859, 859, -4*w^2 + 3*w + 17],\ [863, 863, -4*w^3 + 8*w^2 + 14*w - 21],\ [877, 877, -w^3 - w^2 + 6*w - 1],\ [881, 881, -5*w - 1],\ [883, 883, -4*w^3 + 4*w^2 + 21*w - 13],\ [883, 883, 2*w^3 - 11*w - 1],\ [887, 887, -3*w^3 - w^2 + 8*w - 5],\ [907, 907, w^3 - w^2 - w + 5],\ [911, 911, 2*w^2 - 5*w - 5],\ [919, 919, -w^3 + 3*w^2 + 6*w - 3],\ [919, 919, 5*w^2 + 4*w - 9],\ [929, 929, w^3 + 3*w^2 - 8*w - 17],\ [937, 937, -4*w^3 + 4*w^2 + 17*w - 7],\ [953, 953, -2*w^3 + 2*w^2 + 7*w + 5],\ [953, 953, 3*w^3 - 4*w^2 - 11*w + 3],\ [967, 967, 4*w^3 - 2*w^2 - 17*w + 3],\ [971, 971, w^3 - 3*w^2 - 8*w + 1],\ [983, 983, -2*w^3 - 2*w^2 + 12*w + 13],\ [991, 991, -2*w^3 - 2*w^2 + 8*w + 7],\ [991, 991, w^3 + w^2 - 10*w + 1]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, -1, 1, 2, -2, 4, -8, 6, -4, 4, -4, 12, 4, 12, -10, 10, 12, -14, 6, -14, 6, 18, -8, 16, 2, 14, 0, 20, -2, -4, 10, -6, 2, -4, -12, 24, 8, -2, -18, 10, -16, 14, 10, -2, 26, -26, 28, -10, 2, 22, -6, 16, 18, 14, -4, -16, -16, -10, 2, 30, -28, -24, 6, 18, -2, -2, 4, -34, -32, -24, -16, -32, 16, 22, 18, 14, -26, -6, -34, -4, 20, 0, 0, -18, 28, 6, 2, 14, 22, -22, -38, 14, 32, 8, -20, 4, -10, 4, -30, 36, 20, 4, 18, -26, -6, -42, 20, 2, -28, -20, -18, 6, -36, 14, -22, 30, -14, 12, -12, -10, 32, 24, -2, -20, -32, 6, -52, 42, -18, 10, -10, 12, -44, 14, 14, -8, 24, 12, -34, -46, -6, 6, 38, 28, -48, -2, -46, -12, -52, 48, -12, 32, -8, -56, 42, -10, -18, 10, -40, -12, -24, 16, -32] 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 + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]