/* 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, 5, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([5, 5, w^3 - 4*w]) primes_array = [ [5, 5, w^3 - 4*w],\ [7, 7, w + 1],\ [7, 7, -w^3 + 4*w - 1],\ [13, 13, -w^2 + 3],\ [16, 2, 2],\ [17, 17, w^3 + w^2 - 4*w - 2],\ [17, 17, -w^3 + 5*w - 2],\ [19, 19, -w^2 - w + 4],\ [19, 19, -w^2 - w + 1],\ [29, 29, 2*w^3 - w^2 - 9*w + 5],\ [41, 41, -w^3 + w^2 + 5*w - 3],\ [43, 43, w^3 - w^2 - 4*w + 2],\ [43, 43, w^3 - 6*w],\ [47, 47, -w^3 - w^2 + 5*w],\ [49, 7, w^2 + 2*w - 2],\ [59, 59, 2*w^3 - 8*w + 3],\ [67, 67, w^2 - w - 4],\ [79, 79, w^3 - w^2 - 4*w + 1],\ [81, 3, -3],\ [97, 97, w^3 + w^2 - 5*w + 1],\ [107, 107, -2*w^3 + 3*w^2 + 10*w - 12],\ [109, 109, 2*w^3 - w^2 - 9*w + 3],\ [125, 5, -3*w^3 - w^2 + 12*w + 1],\ [127, 127, -2*w^3 + w^2 + 10*w - 8],\ [137, 137, -w^3 + w^2 + 3*w - 5],\ [139, 139, w^3 - w^2 - 5*w + 1],\ [149, 149, 2*w^2 - w - 6],\ [149, 149, 2*w^3 + w^2 - 9*w],\ [163, 163, w^3 - 5*w - 3],\ [163, 163, 2*w^3 - 7*w],\ [173, 173, -2*w^3 + 11*w - 3],\ [173, 173, -w^3 + w^2 + 4*w - 8],\ [179, 179, 2*w^3 - w^2 - 8*w + 5],\ [181, 181, 2*w^3 - w^2 - 8*w],\ [181, 181, 2*w^3 - 9*w - 3],\ [191, 191, 2*w^2 - 5],\ [191, 191, -2*w^2 - w + 10],\ [193, 193, w^3 + w^2 - 3*w - 4],\ [193, 193, -w^3 + 2*w^2 + 3*w - 3],\ [197, 197, -2*w^3 + 9*w - 4],\ [197, 197, w^2 - 7],\ [199, 199, 3*w^3 - 13*w + 1],\ [199, 199, w^3 + 2*w^2 - 5*w - 7],\ [227, 227, -3*w^3 + w^2 + 13*w - 4],\ [227, 227, -w^3 + 2*w^2 + 7*w - 6],\ [241, 241, -2*w^3 + 7*w - 1],\ [257, 257, -2*w^3 + w^2 + 7*w - 5],\ [257, 257, 2*w^3 - w^2 - 7*w + 2],\ [263, 263, -w^3 + 7*w - 3],\ [269, 269, -2*w^3 + 2*w^2 + 11*w - 8],\ [271, 271, w^2 + 3*w - 2],\ [271, 271, w^2 + 2*w - 7],\ [277, 277, -2*w^3 + 11*w - 2],\ [281, 281, 2*w^3 - 11*w + 1],\ [283, 283, 2*w^3 - 9*w + 5],\ [283, 283, -2*w^3 + w^2 + 11*w - 7],\ [289, 17, -w^3 + 2*w^2 + 4*w - 4],\ [293, 293, -2*w^3 - w^2 + 7*w + 3],\ [307, 307, -3*w^3 + 2*w^2 + 13*w - 9],\ [311, 311, -w^3 + w^2 + 3*w - 7],\ [313, 313, -w^3 + 2*w^2 + 3*w - 2],\ [313, 313, w^2 - w - 8],\ [317, 317, -2*w^3 - w^2 + 9*w - 1],\ [331, 331, w^3 + 2*w^2 - 5*w - 3],\ [337, 337, w^3 + 2*w^2 - 6*w - 4],\ [337, 337, w^3 - 2*w^2 - 6*w + 5],\ [347, 347, 2*w^3 + 2*w^2 - 9*w - 3],\ [347, 347, -2*w^3 + w^2 + 7*w - 4],\ [349, 349, w^2 - 2*w - 4],\ [353, 353, -w^3 + 2*w^2 + 2*w - 6],\ [359, 359, -w^3 + w^2 + 7*w - 6],\ [359, 359, -w^2 - w - 2],\ [361, 19, 2*w^3 - w^2 - 11*w],\ [367, 367, -2*w^3 + 2*w^2 + 8*w - 5],\ [373, 373, w^3 + w^2 - 2*w - 4],\ [379, 379, 2*w^3 - w^2 - 11*w + 4],\ [389, 389, 3*w^2 + w - 11],\ [397, 397, 3*w^3 - 13*w + 5],\ [401, 401, w - 5],\ [409, 409, 3*w^3 - 12*w + 4],\ [409, 409, 3*w^3 + 2*w^2 - 14*w - 4],\ [421, 421, 2*w^3 - w^2 - 10*w + 1],\ [421, 421, w^3 + 2*w^2 - 5*w - 4],\ [439, 439, -2*w^3 + 10*w - 5],\ [443, 443, -2*w^3 + 12*w - 5],\ [443, 443, -4*w^3 + w^2 + 18*w - 9],\ [443, 443, -2*w^3 + w^2 + 7*w - 9],\ [443, 443, 3*w^3 + 2*w^2 - 14*w - 5],\ [449, 449, w^3 + 2*w^2 - 2*w - 6],\ [449, 449, -2*w^3 + w^2 + 11*w - 5],\ [461, 461, 2*w^3 + 2*w^2 - 9*w - 4],\ [467, 467, -w^3 + w^2 + 7*w - 5],\ [487, 487, 2*w^2 + 4*w - 7],\ [491, 491, -w^3 + w^2 + 7*w - 4],\ [503, 503, 2*w^3 + w^2 - 9*w + 2],\ [521, 521, w^2 - 3*w - 3],\ [523, 523, -w^3 + 2*w^2 + 5*w - 4],\ [523, 523, -w^3 + 8*w - 5],\ [563, 563, w^3 + 3*w^2 - w - 8],\ [563, 563, w^3 - 2*w^2 - 8*w + 4],\ [563, 563, -w^3 + w^2 + 2*w - 5],\ [563, 563, -3*w^3 - w^2 + 10*w - 2],\ [577, 577, 3*w^3 - 16*w],\ [587, 587, w^3 + 2*w^2 - 6],\ [587, 587, -w^3 + 4*w - 6],\ [601, 601, -w - 5],\ [607, 607, w^3 - 2*w^2 - 4*w + 1],\ [613, 613, 4*w^3 - 17*w],\ [617, 617, -3*w^3 + w^2 + 14*w - 2],\ [617, 617, -4*w^3 + 17*w - 4],\ [619, 619, -3*w^3 + 12*w - 2],\ [643, 643, 3*w^3 - w^2 - 12*w + 3],\ [643, 643, -2*w^3 - w^2 + 11*w - 2],\ [647, 647, 2*w^3 + w^2 - 9*w + 3],\ [653, 653, w^3 + w^2 - 7*w - 4],\ [661, 661, -w^3 + 4*w^2 + 6*w - 15],\ [661, 661, 3*w^3 - 2*w^2 - 12*w + 10],\ [677, 677, -3*w^2 - 2*w + 12],\ [691, 691, -2*w^3 + 3*w^2 + 11*w - 10],\ [691, 691, -3*w^3 + 16*w - 3],\ [701, 701, 3*w^3 - 13*w + 6],\ [719, 719, -3*w^2 + w + 10],\ [727, 727, w^3 - 3*w^2 - 4*w + 6],\ [743, 743, -w^3 + 2*w^2 + 5*w - 3],\ [761, 761, -w^3 + 3*w^2 + 3*w - 12],\ [761, 761, 3*w^3 - 2*w^2 - 14*w + 7],\ [769, 769, -3*w^3 + 3*w^2 + 16*w - 13],\ [769, 769, w^3 + 2*w^2 - 7*w - 6],\ [773, 773, w^3 - 8*w + 4],\ [773, 773, 4*w^2 + w - 16],\ [787, 787, w^2 + 4*w - 2],\ [797, 797, -2*w^3 + 3*w^2 + 10*w - 10],\ [797, 797, -w^3 - w^2 + 4*w - 4],\ [797, 797, w^3 + 2*w^2 - 3*w - 9],\ [797, 797, -3*w^3 + 3*w^2 + 11*w - 10],\ [821, 821, w^2 + w - 9],\ [827, 827, w^3 - 8*w + 1],\ [827, 827, -2*w^3 + w^2 + 9*w - 11],\ [827, 827, 3*w^3 - 14*w + 5],\ [827, 827, 2*w^3 + w^2 - 7*w - 5],\ [829, 829, -2*w^3 - 2*w^2 + 9*w - 1],\ [839, 839, -3*w^3 + 15*w - 5],\ [853, 853, -4*w^3 + 15*w - 8],\ [853, 853, -w^3 + 2*w^2 + 6*w - 3],\ [859, 859, -w^3 + w^2 + w - 4],\ [859, 859, w^3 + w^2 - w - 5],\ [881, 881, -w^3 + w^2 + 2*w - 6],\ [881, 881, w^3 + w^2 - 2*w - 6],\ [883, 883, w^3 + 3*w^2 - 3*w - 6],\ [887, 887, w^3 + 3*w^2 - 3*w - 8],\ [919, 919, 2*w^3 - w^2 - 13*w],\ [929, 929, -w^3 - 3*w^2 + 2*w + 10],\ [929, 929, w^3 + w^2 - 5*w - 8],\ [941, 941, w^3 + 2*w^2 - 3*w - 10],\ [953, 953, -w^3 + 5*w - 7],\ [953, 953, -2*w^3 + 3*w^2 + 9*w - 9],\ [953, 953, -2*w^3 - w^2 + 10*w - 3],\ [953, 953, -3*w^3 + 11*w - 1],\ [961, 31, -w^3 + 3*w^2 + 2*w - 10],\ [961, 31, -3*w^2 + 2*w + 7],\ [967, 967, w^3 + 3*w^2 - 3*w - 7],\ [967, 967, 4*w^3 + w^2 - 20*w + 1],\ [983, 983, 2*w^3 - w^2 - 12*w + 8],\ [983, 983, 2*w^3 + w^2 - 6*w - 4],\ [991, 991, 2*w^3 - 12*w + 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 4, 2, 4, -1, -4, 2, -4, 2, 4, 4, -6, 0, -8, -2, 2, 4, 0, -14, -2, 6, -2, -14, 4, -6, 12, 12, -18, -20, 8, -22, 14, 4, 0, -2, -8, -12, -2, -14, 10, 2, 10, 10, 24, 12, -24, -2, 16, 4, -6, 8, 8, 10, 2, 16, -24, 14, -6, 4, 18, -16, -2, 18, 10, -8, 34, -8, -2, -10, -16, 20, 16, -12, -18, 10, 16, -18, 2, -2, 14, 32, 0, -32, -32, 24, -4, -24, -36, 34, -14, 4, -4, -8, -8, 32, 30, -18, 36, 4, -28, -26, -14, -34, 20, 36, -26, -28, -34, 48, -18, 24, 40, -32, 16, -46, -2, 14, -26, 18, -36, 22, -24, -2, -30, 26, 18, 34, 32, 22, 30, 28, -6, 42, -30, 38, 26, 8, -12, 36, -48, -46, 0, -54, 20, 40, -20, 32, 46, 34, 22, -56, 42, -22, -42, -34, 0, 6, -50, 20, -52, 36, 28, 36, 24, -40] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5, 5, w^3 - 4*w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]