/* 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([4, 3, -5, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([5, 5, w^3 - 3*w^2 - 3*w + 5]) primes_array = [ [2, 2, w^3 - 3*w^2 - w + 2],\ [5, 5, w^2 - 2*w - 3],\ [5, 5, w^3 - 3*w^2 - 3*w + 5],\ [8, 2, w^3 - 2*w^2 - 3*w + 3],\ [13, 13, -w^2 + w + 3],\ [17, 17, -w^2 + 3*w + 1],\ [23, 23, w^2 - 3],\ [25, 5, -w^2 + 2*w + 1],\ [37, 37, w^3 - 4*w^2 - 2*w + 9],\ [41, 41, w^2 - w - 5],\ [49, 7, -w^3 + 2*w^2 + 2*w - 1],\ [49, 7, w^2 + w - 3],\ [59, 59, w^3 - 3*w^2 - 4*w + 5],\ [67, 67, -w^3 + 3*w^2 + w - 5],\ [71, 71, 2*w - 3],\ [71, 71, w^3 - 4*w^2 + 2*w + 5],\ [79, 79, -w^3 + 5*w^2 - 4*w - 5],\ [79, 79, -2*w^3 + 7*w^2 + 5*w - 15],\ [81, 3, -3],\ [83, 83, -2*w^3 + 6*w^2 + 2*w - 5],\ [97, 97, w^3 - w^2 - 7*w - 3],\ [101, 101, -w^3 + 3*w^2 + 3*w - 3],\ [107, 107, -w^3 + 4*w^2 - 7],\ [113, 113, w^3 - 3*w^2 - 5*w + 3],\ [121, 11, -w^3 + 3*w^2 + 4*w - 3],\ [121, 11, 2*w^3 - 6*w^2 - 3*w + 5],\ [127, 127, -2*w^3 + 6*w^2 + 5*w - 9],\ [137, 137, -w^3 + 5*w^2 + 3*w - 9],\ [139, 139, w^3 - w^2 - 4*w + 1],\ [149, 149, w^3 - 3*w^2 - w + 9],\ [157, 157, w^2 - 4*w + 1],\ [163, 163, -3*w^3 + 7*w^2 + 9*w - 13],\ [163, 163, w^3 - 3*w^2 - w + 7],\ [179, 179, -2*w^3 + 3*w^2 + 5*w - 5],\ [179, 179, -2*w^3 + 4*w^2 + 5*w - 9],\ [181, 181, -w^2 + 3*w - 3],\ [181, 181, 2*w^3 - 4*w^2 - 8*w + 5],\ [191, 191, 2*w - 5],\ [193, 193, -2*w^3 + 4*w^2 + 7*w + 3],\ [193, 193, -2*w^3 + 5*w^2 + 5*w - 7],\ [197, 197, -w^3 + 4*w^2 - 11],\ [199, 199, -2*w^3 + 8*w^2 + 6*w - 15],\ [211, 211, -2*w^3 + 3*w^2 + 6*w - 5],\ [211, 211, -4*w^3 + 10*w^2 + 12*w - 19],\ [229, 229, w^3 - 3*w^2 - 4*w + 9],\ [229, 229, w^2 - 5],\ [233, 233, w^2 - 2*w - 7],\ [239, 239, -3*w^3 + 10*w^2 + 2*w - 9],\ [239, 239, -2*w^3 + 5*w^2 + 5*w - 5],\ [257, 257, -2*w^3 + 5*w^2 + 4*w - 9],\ [263, 263, w^3 - 2*w^2 - 4*w - 3],\ [263, 263, w^3 - 6*w - 7],\ [269, 269, w^3 - 3*w^2 - w - 1],\ [269, 269, w - 5],\ [281, 281, -2*w + 7],\ [293, 293, 2*w^2 - w - 7],\ [293, 293, -2*w^3 + 6*w^2 + 6*w - 9],\ [307, 307, -2*w^3 + 5*w^2 + 4*w - 11],\ [311, 311, -w^3 + 3*w^2 + 2*w - 9],\ [317, 317, 4*w^3 - 15*w^2 + 3*w + 15],\ [317, 317, w^3 - 4*w^2 - 4*w + 9],\ [331, 331, -w^3 + 4*w^2 + 2*w - 11],\ [331, 331, 2*w^3 - 7*w^2 - 5*w + 13],\ [337, 337, 2*w^3 - 4*w^2 - 8*w - 1],\ [347, 347, -2*w^3 + 7*w^2 + 9*w - 9],\ [349, 349, -w^3 + 5*w^2 - 2*w - 11],\ [349, 349, 4*w^3 - 9*w^2 - 14*w + 13],\ [353, 353, -3*w^3 + 7*w^2 + 9*w - 11],\ [367, 367, 3*w^3 - 5*w^2 - 11*w + 5],\ [367, 367, -w^3 + 3*w^2 + 5*w - 1],\ [373, 373, w^3 - 2*w^2 - 6*w + 1],\ [379, 379, 2*w^3 - 5*w^2 - 7*w + 5],\ [383, 383, 2*w^3 - 3*w^2 - 11*w - 1],\ [383, 383, -2*w^3 + 5*w^2 + 3*w - 13],\ [397, 397, -2*w^3 + 4*w^2 + 7*w - 7],\ [397, 397, 2*w^3 - 3*w^2 - 8*w - 5],\ [409, 409, w^3 - 3*w^2 + w - 1],\ [419, 419, -4*w^3 + 14*w^2 - w - 13],\ [421, 421, -3*w^2 + 2*w + 9],\ [421, 421, 2*w^2 - 6*w - 3],\ [431, 431, -2*w^3 + 4*w^2 + 9*w - 7],\ [431, 431, -2*w^3 + 6*w^2 + 3*w - 15],\ [431, 431, -3*w^3 + 6*w^2 + 10*w - 9],\ [431, 431, -3*w^3 + 11*w^2 + 10*w - 19],\ [443, 443, 3*w^3 - 6*w^2 - 8*w + 13],\ [443, 443, -2*w^3 + 5*w^2 + 4*w - 5],\ [443, 443, -2*w^3 + 5*w^2 + 6*w - 3],\ [443, 443, 5*w^3 - 12*w^2 - 16*w + 19],\ [461, 461, w^3 - 2*w^2 + 7],\ [461, 461, -3*w^2 + w + 7],\ [479, 479, w^2 + w - 5],\ [487, 487, 2*w^2 - 4*w + 1],\ [487, 487, 2*w^3 - 8*w^2 + 4*w + 7],\ [491, 491, -3*w^3 + 7*w^2 + 7*w - 1],\ [509, 509, -2*w^3 + 9*w^2 + 5*w - 19],\ [509, 509, -3*w^3 + 6*w^2 + 10*w + 1],\ [521, 521, w^3 - 2*w^2 - 6*w + 3],\ [521, 521, 3*w - 5],\ [523, 523, -w^3 + 5*w^2 + 4*w - 7],\ [523, 523, -2*w^3 + 4*w^2 + 6*w - 1],\ [523, 523, w^2 - 7],\ [523, 523, -2*w^3 + 8*w^2 + 8*w - 13],\ [541, 541, -w^3 + 5*w^2 - w - 13],\ [547, 547, -2*w^3 + 7*w^2 + 3*w - 11],\ [547, 547, -w^3 + 4*w^2 + 2*w - 13],\ [547, 547, -2*w^3 + 2*w^2 + 6*w - 1],\ [547, 547, -w^3 + 6*w^2 - 6*w - 7],\ [563, 563, 2*w^2 - 5*w - 1],\ [563, 563, w^2 - 2*w + 3],\ [569, 569, -2*w - 5],\ [571, 571, -2*w^3 + 6*w^2 + 3*w - 11],\ [577, 577, -w^3 + 3*w^2 - 7],\ [593, 593, w^3 - w^2 - 5*w + 3],\ [601, 601, 2*w^3 - 6*w^2 - 4*w + 5],\ [607, 607, -6*w^2 + 15*w + 13],\ [607, 607, -w^3 + 4*w^2 - 2*w - 7],\ [613, 613, -2*w^3 + 6*w^2 + 2*w - 9],\ [617, 617, -3*w^3 + 9*w^2 + 5*w - 9],\ [617, 617, 3*w^3 - 6*w^2 - 12*w + 7],\ [619, 619, -2*w^3 + 8*w^2 + 7*w - 13],\ [619, 619, 2*w^3 - 4*w^2 - 5*w + 1],\ [641, 641, 2*w^3 - w^2 - 6*w + 1],\ [641, 641, -2*w^3 + 4*w^2 + 8*w - 7],\ [641, 641, -2*w^3 + 7*w^2 + 4*w - 13],\ [641, 641, -2*w^3 + 3*w^2 + 7*w - 1],\ [647, 647, -2*w^3 + 7*w^2 + 8*w - 11],\ [647, 647, -2*w^3 + 4*w^2 + 6*w - 3],\ [653, 653, -4*w^2 + 3*w + 13],\ [653, 653, 3*w^3 - 7*w^2 - 11*w + 7],\ [659, 659, -5*w^3 + 14*w^2 + 16*w - 25],\ [659, 659, -4*w^3 + 13*w^2 + 11*w - 25],\ [673, 673, 2*w^3 - 7*w^2 - 6*w + 15],\ [677, 677, 3*w^3 - 8*w^2 - 6*w + 11],\ [677, 677, w^3 - 5*w^2 + 2*w + 9],\ [683, 683, 2*w^2 - 5*w - 9],\ [683, 683, w^3 - w^2 - 4*w - 7],\ [709, 709, -2*w^3 + 6*w^2 + 4*w - 3],\ [733, 733, -2*w^3 + 5*w^2 + 3*w + 1],\ [733, 733, 2*w^3 - 2*w^2 - 9*w - 1],\ [739, 739, -w - 5],\ [751, 751, 3*w^3 - 7*w^2 - 7*w + 11],\ [757, 757, -2*w^3 + 3*w^2 + 8*w - 3],\ [757, 757, 2*w^3 - 3*w^2 - 12*w - 3],\ [761, 761, -3*w^3 + 7*w^2 + 12*w - 11],\ [761, 761, -3*w^3 + 9*w^2 + 6*w - 11],\ [787, 787, -3*w^3 + 5*w^2 + 12*w + 3],\ [787, 787, w^2 - w - 9],\ [797, 797, -3*w^3 + 7*w^2 + 6*w - 17],\ [827, 827, -2*w^3 + 4*w^2 + 9*w - 11],\ [827, 827, -6*w^3 + 17*w^2 + 19*w - 29],\ [853, 853, -3*w^3 + 10*w^2 + 6*w - 21],\ [857, 857, 3*w^3 - 12*w^2 + 4*w + 9],\ [857, 857, -3*w^3 + 9*w^2 + 4*w - 13],\ [863, 863, -3*w^3 + 10*w^2 + 4*w - 15],\ [863, 863, -4*w^2 + w + 11],\ [877, 877, -2*w^3 + 4*w^2 + 8*w - 9],\ [881, 881, -2*w^3 + 4*w^2 + 5*w - 3],\ [907, 907, -w^3 + 5*w^2 - 2*w - 15],\ [907, 907, -2*w^3 + 6*w^2 + 7*w - 15],\ [929, 929, -w^2 + 11],\ [929, 929, -2*w^3 + 6*w^2 + 3*w - 13],\ [937, 937, -3*w^3 + 7*w^2 + 8*w - 3],\ [941, 941, w^3 + w^2 - 8*w - 5],\ [953, 953, 4*w^2 - 8*w - 13],\ [953, 953, w^3 - 4*w^2 - 4*w + 3],\ [967, 967, 3*w^2 - 5*w - 9],\ [971, 971, 3*w^2 - 4*w - 7],\ [971, 971, w^3 - 5*w^2 - 4*w + 11],\ [977, 977, -3*w^3 + 11*w^2 + 6*w - 25],\ [983, 983, -2*w^3 + 8*w^2 + 3*w - 21],\ [991, 991, 2*w^3 - 4*w^2 - 10*w + 3],\ [991, 991, 2*w^3 - 8*w^2 - 3*w + 19],\ [997, 997, -4*w^3 + 10*w^2 + 11*w - 21]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 2, 1, -1, 2, -6, -8, -2, -6, 6, 10, -2, 0, -16, 0, -16, -8, 12, 2, 0, 6, -18, -4, 6, -14, 10, -8, -10, 4, -6, -2, -4, -4, 12, -20, 2, 10, -12, 2, -2, -18, -16, 20, -16, 2, -14, -22, 4, 16, 18, 12, 16, -10, 6, 10, -6, 2, 4, 24, -22, -14, 4, 36, 22, 20, 34, -6, -18, -16, 0, -10, 20, 4, 24, -14, 2, -10, -8, 26, 10, -24, -32, -12, -32, 4, 24, 4, -12, 18, 42, 8, 24, -8, -24, -14, -38, -6, -18, -16, -4, 8, -12, 22, -20, -36, -24, -12, -20, -28, -30, 40, -10, 30, -30, 32, -36, -2, -6, 42, -12, 28, -30, -18, 2, -18, -24, -32, 18, 6, 28, 4, 14, 38, 42, 24, 4, -30, 14, 26, 44, 48, 42, 18, -22, -34, 4, -12, -50, -36, 44, 14, -18, 10, 44, 20, -14, 30, 28, 32, -6, 2, 22, -38, 46, -38, 52, -36, -36, 26, -60, 8, 8, -2] 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 - 3*w^2 - 3*w + 5])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]