/* 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, 0, -6, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([20, 10, -w^2 + 2*w + 4]) primes_array = [ [2, 2, w],\ [5, 5, -w^3 + 3*w^2 + 2*w - 1],\ [5, 5, w - 1],\ [11, 11, w^3 - 2*w^2 - 5*w - 1],\ [13, 13, -w^3 + 3*w^2 + 3*w - 1],\ [17, 17, 2*w^3 - 5*w^2 - 9*w + 5],\ [23, 23, -w^3 + 3*w^2 + 4*w - 5],\ [25, 5, -w^2 + 3*w + 1],\ [29, 29, -2*w^3 + 6*w^2 + 5*w - 1],\ [31, 31, -w^2 + 2*w + 1],\ [43, 43, -w^3 + 3*w^2 + 2*w - 3],\ [43, 43, -w^3 + 2*w^2 + 6*w - 3],\ [59, 59, 2*w^3 - 6*w^2 - 7*w + 7],\ [73, 73, 3*w^3 - 6*w^2 - 16*w - 5],\ [79, 79, -5*w^3 + 14*w^2 + 20*w - 17],\ [81, 3, -3],\ [83, 83, -w - 3],\ [83, 83, w^2 - 3*w - 7],\ [89, 89, w^2 - 2*w - 7],\ [101, 101, -2*w^3 + 5*w^2 + 8*w - 3],\ [101, 101, 5*w^3 - 14*w^2 - 19*w + 17],\ [103, 103, -w^3 + w^2 + 8*w + 3],\ [103, 103, 2*w^3 - 5*w^2 - 7*w - 1],\ [109, 109, 3*w^3 - 7*w^2 - 14*w + 1],\ [109, 109, -w^2 + 4*w + 1],\ [127, 127, -3*w^3 + 8*w^2 + 11*w - 7],\ [127, 127, -w^3 + 2*w^2 + 7*w + 1],\ [137, 137, -2*w^3 + 5*w^2 + 9*w - 1],\ [139, 139, -w^3 + 3*w^2 + 2*w - 5],\ [149, 149, w^3 - 3*w^2 - w - 1],\ [149, 149, -2*w^3 + 4*w^2 + 10*w + 1],\ [163, 163, w^3 - 4*w^2 - w + 11],\ [163, 163, 2*w^3 - 4*w^2 - 10*w + 1],\ [173, 173, -4*w^3 + 11*w^2 + 15*w - 13],\ [179, 179, 2*w^2 - 6*w - 3],\ [179, 179, -w^3 + 2*w^2 + 7*w - 1],\ [181, 181, w^3 - 10*w - 9],\ [181, 181, -3*w^3 + 8*w^2 + 14*w - 7],\ [199, 199, w^3 - 8*w - 9],\ [211, 211, 2*w - 3],\ [223, 223, -w^3 + 4*w^2 + w - 5],\ [227, 227, w^3 - 2*w^2 - 5*w - 5],\ [227, 227, -3*w^3 + 7*w^2 + 14*w - 5],\ [227, 227, -4*w^3 + 10*w^2 + 19*w - 7],\ [227, 227, w^2 - 4*w - 5],\ [239, 239, -2*w^3 + 5*w^2 + 7*w - 3],\ [251, 251, -w^3 + 4*w^2 + 2*w - 11],\ [251, 251, 2*w^3 - 6*w^2 - 6*w + 1],\ [257, 257, -3*w^3 + 6*w^2 + 16*w + 3],\ [263, 263, -w^3 + 3*w^2 + 3*w - 7],\ [263, 263, w^3 - 4*w^2 + 7],\ [269, 269, -2*w^3 + 6*w^2 + 6*w - 11],\ [269, 269, -w^3 + 4*w^2 - w - 5],\ [271, 271, -3*w^3 + 9*w^2 + 11*w - 11],\ [271, 271, w^2 - 5*w - 3],\ [277, 277, w^3 - 4*w^2 - 2*w + 7],\ [277, 277, -2*w^3 + 7*w^2 + 8*w - 9],\ [281, 281, 2*w^2 - 4*w - 5],\ [281, 281, 2*w^3 - 4*w^2 - 11*w + 1],\ [283, 283, -3*w^3 + 8*w^2 + 14*w - 11],\ [293, 293, w^3 - 2*w^2 - 6*w + 5],\ [307, 307, -2*w^3 + 5*w^2 + 7*w - 1],\ [313, 313, 2*w^3 - 4*w^2 - 9*w + 3],\ [313, 313, -2*w^3 + 5*w^2 + 6*w - 3],\ [317, 317, -2*w^3 + 5*w^2 + 9*w + 1],\ [347, 347, 4*w^3 - 9*w^2 - 21*w + 3],\ [347, 347, 4*w^3 - 10*w^2 - 18*w + 5],\ [349, 349, -2*w^3 + 6*w^2 + 7*w - 3],\ [353, 353, -w^3 + 12*w + 5],\ [353, 353, w^2 - w - 7],\ [359, 359, -2*w^3 + 5*w^2 + 6*w - 7],\ [359, 359, -w^3 + 4*w^2 - 11],\ [373, 373, -w^3 + 2*w^2 + 6*w + 5],\ [379, 379, -3*w^3 + 8*w^2 + 14*w - 5],\ [397, 397, 6*w^3 - 14*w^2 - 30*w + 7],\ [401, 401, 3*w^3 - 5*w^2 - 20*w - 7],\ [409, 409, 3*w^3 - 7*w^2 - 12*w - 3],\ [409, 409, 2*w^2 - 4*w - 7],\ [421, 421, w^3 - 11*w - 11],\ [421, 421, -w^3 + 3*w^2 + w - 7],\ [431, 431, 2*w^3 - 3*w^2 - 14*w - 3],\ [431, 431, -4*w^3 + 11*w^2 + 15*w - 15],\ [433, 433, 2*w^3 - 5*w^2 - 6*w + 1],\ [439, 439, -4*w^3 + 11*w^2 + 13*w - 9],\ [439, 439, -2*w^3 + 6*w^2 + 8*w - 11],\ [443, 443, 2*w - 5],\ [443, 443, -6*w^3 + 17*w^2 + 24*w - 21],\ [449, 449, w^3 - 2*w^2 - 8*w + 3],\ [449, 449, 4*w^3 - 12*w^2 - 15*w + 17],\ [457, 457, -2*w^3 + 4*w^2 + 9*w + 5],\ [461, 461, -3*w^3 + 6*w^2 + 15*w - 1],\ [461, 461, -3*w^3 + 7*w^2 + 17*w + 1],\ [463, 463, -4*w^3 + 10*w^2 + 17*w - 7],\ [463, 463, -3*w^3 + 10*w^2 + 9*w - 17],\ [467, 467, 4*w^3 - 8*w^2 - 21*w - 7],\ [467, 467, w^3 - 6*w^2 + 3*w + 19],\ [479, 479, -w^3 + w^2 + 8*w + 1],\ [487, 487, -4*w^3 + 11*w^2 + 14*w - 15],\ [487, 487, 3*w^3 - 6*w^2 - 15*w - 5],\ [491, 491, w^2 - 5],\ [503, 503, 2*w^3 - 5*w^2 - 11*w + 3],\ [523, 523, -3*w^3 + 7*w^2 + 13*w + 1],\ [547, 547, 2*w^3 - 3*w^2 - 12*w - 3],\ [547, 547, 2*w^3 - 3*w^2 - 12*w - 9],\ [557, 557, -3*w^3 + 9*w^2 + 9*w - 11],\ [557, 557, -6*w^3 + 15*w^2 + 27*w - 13],\ [563, 563, -3*w^3 + 7*w^2 + 14*w - 7],\ [571, 571, -5*w^3 + 11*w^2 + 26*w - 3],\ [593, 593, -6*w^3 + 15*w^2 + 26*w - 7],\ [599, 599, 7*w^3 - 18*w^2 - 29*w + 17],\ [599, 599, -2*w^3 + 6*w^2 + 8*w - 3],\ [601, 601, -7*w^3 + 20*w^2 + 28*w - 23],\ [601, 601, 3*w^3 - 7*w^2 - 12*w + 5],\ [607, 607, 5*w^3 - 12*w^2 - 24*w + 9],\ [607, 607, w^3 - 5*w^2 + 15],\ [613, 613, -w^3 + 5*w^2 - 2*w - 9],\ [617, 617, w^3 + w^2 - 13*w - 15],\ [617, 617, 2*w^3 - 4*w^2 - 8*w - 1],\ [619, 619, 5*w^3 - 10*w^2 - 27*w - 7],\ [619, 619, 2*w^3 - 4*w^2 - 10*w + 3],\ [643, 643, w^3 - 5*w^2 + 5*w + 5],\ [643, 643, 4*w^3 - 9*w^2 - 20*w - 1],\ [643, 643, 3*w^3 - 7*w^2 - 14*w - 3],\ [643, 643, -3*w^3 + 7*w^2 + 13*w - 3],\ [647, 647, -3*w^3 + 8*w^2 + 12*w - 3],\ [653, 653, -w^3 + 9*w + 13],\ [653, 653, -w^3 + 4*w^2 + 3*w - 9],\ [653, 653, -2*w^3 + 7*w^2 + 4*w - 7],\ [653, 653, w^2 - 4*w - 9],\ [673, 673, -w^3 + 5*w^2 + w - 13],\ [683, 683, w^3 - 3*w^2 - 3*w - 3],\ [701, 701, 5*w^3 - 13*w^2 - 23*w + 9],\ [709, 709, 2*w^3 - w^2 - 19*w - 15],\ [719, 719, -5*w^3 + 15*w^2 + 20*w - 19],\ [727, 727, -w - 5],\ [751, 751, -4*w^3 + 10*w^2 + 15*w - 9],\ [751, 751, 6*w^3 - 17*w^2 - 22*w + 21],\ [757, 757, 3*w^3 - 6*w^2 - 18*w - 1],\ [757, 757, -w^3 + 4*w^2 + 2*w + 1],\ [769, 769, w^2 - 2*w + 3],\ [773, 773, 5*w^3 - 12*w^2 - 23*w + 9],\ [787, 787, 2*w^3 - 4*w^2 - 5*w + 1],\ [797, 797, -3*w^3 + 8*w^2 + 10*w - 3],\ [809, 809, 2*w^2 - 5*w - 1],\ [809, 809, 4*w^3 - 6*w^2 - 28*w - 11],\ [827, 827, 4*w^3 - 8*w^2 - 22*w - 1],\ [827, 827, 2*w^2 - 6*w - 9],\ [829, 829, -w^3 + w^2 + 10*w + 1],\ [839, 839, -2*w^3 + 2*w^2 + 16*w + 7],\ [877, 877, 6*w^3 - 16*w^2 - 25*w + 13],\ [877, 877, w^3 - w^2 - 7*w + 1],\ [881, 881, 2*w^3 - 2*w^2 - 15*w - 7],\ [881, 881, -4*w^3 + 7*w^2 + 26*w + 9],\ [887, 887, 2*w^3 - 4*w^2 - 13*w - 1],\ [907, 907, 5*w^3 - 11*w^2 - 26*w - 1],\ [907, 907, 5*w^3 - 13*w^2 - 22*w + 9],\ [907, 907, w^3 - 5*w^2 + 2*w + 13],\ [907, 907, -2*w^3 + 7*w^2 + 5*w - 7],\ [911, 911, -3*w^3 + 8*w^2 + 9*w - 5],\ [919, 919, -2*w^3 + 7*w^2 + 6*w - 3],\ [919, 919, -3*w^3 + 8*w^2 + 15*w - 7],\ [947, 947, -2*w^3 + 5*w^2 + 12*w - 9],\ [947, 947, -w^2 + w - 3],\ [947, 947, 3*w^3 - 6*w^2 - 14*w - 7],\ [947, 947, -w^3 + 5*w^2 - w - 17],\ [953, 953, 3*w^3 - 9*w^2 - 9*w + 13],\ [953, 953, -4*w^3 + 13*w^2 + 11*w - 23],\ [967, 967, 8*w^3 - 20*w^2 - 33*w + 19]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 0, -1, -4, 0, 4, -8, 4, -8, 8, 4, -12, 12, 4, -8, -2, -12, 4, -10, 0, -6, 0, 16, 0, 8, 8, -16, 20, 12, 10, 16, 4, 4, 14, -12, 12, 22, -16, 8, -4, -24, -28, -20, 4, 12, -24, -4, -12, 12, -16, 0, -18, 14, -8, 24, 10, -10, -10, -4, -28, 26, 12, -4, 28, 0, 20, -28, -16, 12, -30, -8, -16, 22, 28, -8, 28, 28, -10, -6, -26, -40, -32, -28, 32, 0, 20, 28, 12, -18, 10, -16, -24, -8, -24, -4, -4, 0, -24, 40, -36, -16, 12, 4, -4, 18, -16, 4, -20, -12, -32, 0, -42, 4, 32, -8, -38, 42, -12, -28, -4, -4, -36, -28, 28, 0, 18, -18, 18, -18, 14, -36, -8, -38, -32, 16, -24, 40, -16, 10, -50, -48, 20, 32, 12, -52, 44, -12, -56, -8, -32, 24, -20, 36, -8, -20, -28, 20, -44, 0, 16, 40, -20, 36, -36, -4, -6, -42, -8] 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])] = -1 AL_eigenvalues[ZF.ideal([5, 5, w - 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]