/* 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, -2, 5, 4, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([13, 13, -w^3 + 3*w]) primes_array = [ [7, 7, w^5 - 5*w^3 + 4*w],\ [13, 13, -w^3 + 3*w],\ [25, 5, w^4 - w^3 - 4*w^2 + 2*w + 2],\ [31, 31, -w^5 + 5*w^3 - 5*w + 1],\ [31, 31, -w^4 + w^3 + 5*w^2 - 3*w - 3],\ [37, 37, w^4 - 5*w^2 + w + 3],\ [43, 43, -2*w^5 + w^4 + 9*w^3 - 3*w^2 - 6*w],\ [47, 47, w^5 - w^4 - 4*w^3 + 4*w^2 - 2],\ [49, 7, -w^4 + 4*w^2 + w - 3],\ [53, 53, -w^4 + w^3 + 4*w^2 - 3*w - 4],\ [59, 59, w^4 - 5*w^2 - w + 5],\ [61, 61, w^3 - w^2 - 3*w],\ [64, 2, -2],\ [67, 67, -2*w^5 + w^4 + 9*w^3 - 3*w^2 - 7*w],\ [67, 67, 2*w^5 - w^4 - 10*w^3 + 4*w^2 + 9*w - 1],\ [73, 73, w^5 - w^4 - 4*w^3 + 5*w^2 + w - 3],\ [73, 73, 3*w^5 - 3*w^4 - 13*w^3 + 11*w^2 + 7*w - 3],\ [83, 83, -2*w^5 + 3*w^4 + 9*w^3 - 11*w^2 - 6*w + 2],\ [97, 97, -2*w^4 + w^3 + 9*w^2 - 3*w - 4],\ [101, 101, -2*w^5 + 3*w^4 + 9*w^3 - 11*w^2 - 6*w + 4],\ [101, 101, w^5 - 2*w^4 - 4*w^3 + 9*w^2 + w - 4],\ [107, 107, -2*w^5 + w^4 + 10*w^3 - 4*w^2 - 9*w + 2],\ [107, 107, -w^5 + w^4 + 6*w^3 - 4*w^2 - 8*w + 2],\ [113, 113, w^5 - w^4 - 4*w^3 + 3*w^2 + 2*w + 2],\ [121, 11, w^5 - w^4 - 5*w^3 + 3*w^2 + 5*w - 2],\ [127, 127, 2*w^5 - 3*w^4 - 9*w^3 + 12*w^2 + 5*w - 4],\ [131, 131, w^5 - w^4 - 6*w^3 + 4*w^2 + 8*w - 1],\ [131, 131, 2*w^5 - 3*w^4 - 7*w^3 + 12*w^2 - w - 4],\ [149, 149, -2*w^5 + 2*w^4 + 8*w^3 - 8*w^2 - 3*w + 4],\ [151, 151, w^5 - 2*w^4 - 4*w^3 + 8*w^2 + 3*w - 3],\ [157, 157, w^5 - w^4 - 4*w^3 + 5*w^2 - w - 2],\ [163, 163, -2*w^5 + 2*w^4 + 9*w^3 - 6*w^2 - 6*w],\ [163, 163, w^5 - 2*w^4 - 4*w^3 + 8*w^2 - 4],\ [163, 163, -2*w^5 + w^4 + 9*w^3 - 4*w^2 - 7*w + 4],\ [173, 173, 2*w^4 - w^3 - 8*w^2 + 2*w + 4],\ [173, 173, -w^5 + 3*w^4 + 4*w^3 - 14*w^2 - w + 9],\ [179, 179, -w^5 + 2*w^4 + 4*w^3 - 8*w^2 + 6],\ [191, 191, 2*w^4 - 2*w^3 - 9*w^2 + 6*w + 5],\ [193, 193, -w^5 + w^4 + 5*w^3 - 4*w^2 - 6*w + 2],\ [199, 199, -2*w^5 + 3*w^4 + 9*w^3 - 11*w^2 - 6*w + 3],\ [211, 211, -w^5 + 5*w^3 - 2*w - 2],\ [211, 211, -2*w^5 + w^4 + 9*w^3 - 4*w^2 - 5*w + 1],\ [211, 211, w^5 - 5*w^3 - 2*w^2 + 4*w + 4],\ [223, 223, w^5 - 5*w^3 - w^2 + 7*w + 1],\ [227, 227, -w^5 + w^4 + 6*w^3 - 4*w^2 - 7*w + 1],\ [227, 227, w^3 - 2*w^2 - 4*w + 3],\ [229, 229, -w^5 + 6*w^3 - 7*w + 1],\ [233, 233, 3*w^5 - 2*w^4 - 15*w^3 + 8*w^2 + 13*w - 3],\ [233, 233, -w^5 + 4*w^3 + w^2 - 2*w - 3],\ [233, 233, -w^3 + w^2 + 4*w - 1],\ [257, 257, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 4*w - 2],\ [257, 257, w^5 + w^4 - 6*w^3 - 4*w^2 + 6*w + 1],\ [263, 263, 3*w^5 - 3*w^4 - 13*w^3 + 10*w^2 + 7*w - 1],\ [269, 269, w^5 - w^4 - 4*w^3 + 5*w^2 - 3],\ [283, 283, w^5 - w^4 - 5*w^3 + 5*w^2 + 5*w - 1],\ [293, 293, -2*w^4 + w^3 + 8*w^2 - 3*w - 4],\ [293, 293, 2*w^5 - 4*w^4 - 8*w^3 + 17*w^2 + 3*w - 8],\ [307, 307, w^5 - 7*w^3 + 11*w - 1],\ [311, 311, w^4 - 2*w^3 - 4*w^2 + 8*w + 1],\ [313, 313, -w^5 + 5*w^3 + w^2 - 3*w - 3],\ [317, 317, -w^5 + 4*w^3 - w^2 - w + 4],\ [317, 317, -3*w^5 + 4*w^4 + 13*w^3 - 16*w^2 - 6*w + 8],\ [331, 331, w^5 - 7*w^3 + 10*w],\ [331, 331, 3*w^4 - 2*w^3 - 13*w^2 + 7*w + 7],\ [331, 331, w^5 - 4*w^3 + w^2 + w - 3],\ [343, 7, -4*w^5 + 3*w^4 + 19*w^3 - 10*w^2 - 15*w + 2],\ [347, 347, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 7*w],\ [349, 349, 3*w^5 - 2*w^4 - 14*w^3 + 7*w^2 + 9*w + 1],\ [349, 349, -w^5 + 2*w^4 + 3*w^3 - 9*w^2 + w + 7],\ [359, 359, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 10*w - 4],\ [359, 359, w^5 - 7*w^3 + 11*w + 1],\ [373, 373, w^5 - 6*w^3 + 6*w - 2],\ [383, 383, -4*w^5 + 4*w^4 + 18*w^3 - 14*w^2 - 12*w + 3],\ [389, 389, w^5 + w^4 - 5*w^3 - 5*w^2 + 6*w + 4],\ [397, 397, 2*w^5 - w^4 - 9*w^3 + 5*w^2 + 6*w - 5],\ [397, 397, -2*w^5 + 3*w^4 + 8*w^3 - 10*w^2 - 3*w + 3],\ [409, 409, -w^5 + w^4 + 5*w^3 - 3*w^2 - 6*w - 3],\ [421, 421, -3*w^5 + w^4 + 14*w^3 - 3*w^2 - 10*w - 2],\ [431, 431, 2*w^4 - w^3 - 10*w^2 + 3*w + 7],\ [433, 433, -3*w^5 + 2*w^4 + 14*w^3 - 6*w^2 - 11*w + 2],\ [433, 433, 2*w^5 - 3*w^4 - 10*w^3 + 11*w^2 + 10*w - 2],\ [439, 439, -2*w^5 + 2*w^4 + 10*w^3 - 8*w^2 - 7*w + 3],\ [439, 439, 3*w^5 - 4*w^4 - 13*w^3 + 16*w^2 + 8*w - 5],\ [439, 439, -w^5 + w^4 + 5*w^3 - 6*w^2 - 4*w + 6],\ [461, 461, w^5 + w^4 - 5*w^3 - 4*w^2 + 6*w + 1],\ [467, 467, w^5 + w^4 - 4*w^3 - 6*w^2 + w + 5],\ [479, 479, w^5 - w^4 - 5*w^3 + 3*w^2 + 2*w + 1],\ [487, 487, 3*w^5 - 3*w^4 - 13*w^3 + 12*w^2 + 7*w - 3],\ [499, 499, 2*w^5 - 2*w^4 - 11*w^3 + 7*w^2 + 12*w - 1],\ [503, 503, w^5 - 2*w^4 - 5*w^3 + 9*w^2 + 5*w - 3],\ [509, 509, 3*w^5 - 3*w^4 - 15*w^3 + 11*w^2 + 13*w - 2],\ [509, 509, 2*w^5 - 2*w^4 - 10*w^3 + 7*w^2 + 11*w - 2],\ [521, 521, 3*w^5 - 3*w^4 - 14*w^3 + 10*w^2 + 11*w - 3],\ [521, 521, -w^5 + 2*w^4 + 5*w^3 - 6*w^2 - 5*w],\ [523, 523, -2*w^5 + 2*w^4 + 10*w^3 - 7*w^2 - 11*w + 1],\ [523, 523, -2*w^5 + w^4 + 10*w^3 - 3*w^2 - 11*w],\ [523, 523, -2*w^5 + w^4 + 10*w^3 - 4*w^2 - 10*w + 4],\ [547, 547, -2*w^4 + 2*w^3 + 10*w^2 - 6*w - 7],\ [557, 557, 3*w^5 - 3*w^4 - 14*w^3 + 10*w^2 + 9*w - 1],\ [569, 569, 3*w^5 - 4*w^4 - 13*w^3 + 14*w^2 + 8*w - 2],\ [571, 571, w^4 + w^3 - 5*w^2 - 2*w + 5],\ [577, 577, 3*w^4 - 2*w^3 - 13*w^2 + 7*w + 6],\ [577, 577, w^5 + w^4 - 5*w^3 - 4*w^2 + 4*w + 4],\ [587, 587, 2*w^5 - w^4 - 10*w^3 + 5*w^2 + 9*w - 4],\ [599, 599, -2*w^5 + 3*w^4 + 10*w^3 - 12*w^2 - 9*w + 3],\ [599, 599, w^5 + 2*w^4 - 6*w^3 - 9*w^2 + 8*w + 6],\ [601, 601, -2*w^5 + 3*w^4 + 8*w^3 - 11*w^2 - 5*w + 4],\ [607, 607, w^5 - 2*w^4 - 5*w^3 + 8*w^2 + 3*w - 1],\ [613, 613, w^5 - 2*w^4 - 5*w^3 + 10*w^2 + 5*w - 7],\ [613, 613, -w^5 + 2*w^4 + 3*w^3 - 7*w^2],\ [617, 617, -3*w^5 + 3*w^4 + 12*w^3 - 11*w^2 - 5*w + 4],\ [625, 5, -2*w^5 + 2*w^4 + 9*w^3 - 6*w^2 - 5*w + 1],\ [631, 631, -2*w^5 + w^4 + 9*w^3 - 3*w^2 - 8*w + 1],\ [641, 641, w^5 - 5*w^3 - w^2 + 5*w + 5],\ [659, 659, -w^5 + 3*w^4 + 5*w^3 - 12*w^2 - 5*w + 3],\ [661, 661, 4*w^5 - 3*w^4 - 19*w^3 + 11*w^2 + 14*w - 2],\ [677, 677, -2*w^5 + 2*w^4 + 9*w^3 - 7*w^2 - 6*w - 2],\ [683, 683, -w^5 + w^4 + 4*w^3 - 5*w^2 + w + 4],\ [683, 683, -2*w^4 + w^3 + 9*w^2 - 5*w - 4],\ [701, 701, -2*w^5 + 3*w^4 + 10*w^3 - 11*w^2 - 10*w + 4],\ [701, 701, -3*w^5 + w^4 + 15*w^3 - 3*w^2 - 14*w + 1],\ [709, 709, 2*w^4 - 2*w^3 - 9*w^2 + 5*w + 7],\ [719, 719, w^4 - 2*w^3 - 4*w^2 + 7*w + 4],\ [719, 719, w^3 + 2*w^2 - 4*w - 5],\ [727, 727, 2*w^5 - 3*w^4 - 8*w^3 + 11*w^2 + 4*w - 1],\ [729, 3, -3],\ [743, 743, 3*w^5 - 2*w^4 - 15*w^3 + 6*w^2 + 12*w],\ [743, 743, -w^4 + w^3 + 6*w^2 - 4*w - 3],\ [769, 769, 2*w^5 - 3*w^4 - 8*w^3 + 12*w^2 + 3*w - 2],\ [769, 769, -3*w^5 + 4*w^4 + 13*w^3 - 15*w^2 - 8*w + 3],\ [787, 787, 2*w^3 - w^2 - 5*w],\ [797, 797, 3*w^5 - w^4 - 15*w^3 + 4*w^2 + 12*w - 1],\ [827, 827, 3*w^4 - w^3 - 13*w^2 + 2*w + 8],\ [839, 839, -2*w^5 + w^4 + 10*w^3 - 4*w^2 - 11*w + 2],\ [853, 853, -2*w^4 + w^3 + 10*w^2 - 4*w - 6],\ [853, 853, -w^5 + w^4 + 6*w^3 - 3*w^2 - 7*w - 3],\ [853, 853, -2*w^5 + 3*w^4 + 9*w^3 - 11*w^2 - 8*w + 3],\ [857, 857, w^5 - 2*w^4 - 3*w^3 + 10*w^2 - 2*w - 7],\ [859, 859, -4*w^5 + 3*w^4 + 18*w^3 - 10*w^2 - 12*w],\ [863, 863, w^5 - 3*w^4 - 3*w^3 + 14*w^2 - 2*w - 9],\ [877, 877, -w^5 + 7*w^3 - 12*w - 1],\ [881, 881, 2*w^4 - 2*w^3 - 9*w^2 + 8*w + 6],\ [881, 881, 3*w^5 - w^4 - 15*w^3 + 4*w^2 + 12*w - 2],\ [887, 887, -w^5 - w^4 + 5*w^3 + 5*w^2 - 2*w - 4],\ [919, 919, 4*w^5 - 4*w^4 - 18*w^3 + 14*w^2 + 11*w - 3],\ [919, 919, -w^5 + 4*w^3 - w - 3],\ [929, 929, -w^5 + 2*w^4 + 4*w^3 - 10*w^2 + 5],\ [937, 937, 3*w^5 - 4*w^4 - 12*w^3 + 15*w^2 + 5*w - 3],\ [947, 947, 3*w^5 - 3*w^4 - 13*w^3 + 10*w^2 + 8*w - 4],\ [953, 953, 2*w^5 - 9*w^3 - w^2 + 6*w + 4],\ [953, 953, -3*w^5 + 3*w^4 + 12*w^3 - 11*w^2 - 5*w + 2],\ [967, 967, -2*w^5 + 9*w^3 + 2*w^2 - 7*w - 4],\ [977, 977, 3*w^5 - w^4 - 14*w^3 + 3*w^2 + 11*w - 1],\ [977, 977, w^4 - w^3 - 6*w^2 + 3*w + 3],\ [997, 997, 3*w^5 - 2*w^4 - 15*w^3 + 7*w^2 + 13*w - 4]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-3, 1, 3, -10, -7, -5, -8, -1, -6, 6, -4, -9, -13, 10, -2, 0, -12, -3, -4, 15, -12, -10, -10, 0, -8, -5, -2, 16, 4, -10, 4, -8, 3, -13, -9, 8, 2, -6, 5, 24, 20, -4, 16, 22, 9, -16, 19, -18, 6, 3, -14, 14, -23, -22, -4, -24, 14, -16, -11, 26, -10, 18, 1, 6, -17, 6, 0, 29, -8, 20, 25, 14, 24, -24, -27, -22, -10, 38, -7, -30, -16, -13, -16, 38, -15, 23, -39, -28, 19, 10, 4, -5, 9, 3, -27, -11, 20, 23, 24, 24, -15, 18, 16, 15, 29, 11, -20, 43, -22, -47, 18, -8, 7, 8, 34, -28, 6, 20, -36, -7, 3, -1, -20, -27, -48, -4, 36, 18, -21, -30, 12, -22, 0, 34, -30, -35, 46, 17, 36, -28, -18, 6, 22, -36, -15, -21, 49, 12, 3, -9, -51, -4, -15, -28, 46] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([13, 13, -w^3 + 3*w])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]