/* 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([3, 4, -4, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([5, 5, -w + 2]) primes_array = [ [2, 2, w - 1],\ [3, 3, w],\ [5, 5, -w + 2],\ [11, 11, w + 2],\ [27, 3, -w^3 + 2*w^2 + 4*w - 4],\ [29, 29, -w^2 + 3*w + 1],\ [31, 31, w^3 - 2*w^2 - 2*w + 2],\ [31, 31, -w^2 + 2*w + 4],\ [47, 47, w^3 - w^2 - 4*w + 1],\ [49, 7, 2*w^3 - 2*w^2 - 8*w - 1],\ [49, 7, w^3 - w^2 - 3*w - 2],\ [53, 53, w^3 - 3*w^2 - w + 2],\ [53, 53, w^3 - 5*w - 5],\ [61, 61, 2*w - 1],\ [61, 61, -w^3 + 4*w^2 - 4],\ [67, 67, 3*w^3 - 3*w^2 - 13*w - 4],\ [73, 73, -w^3 + 4*w^2 - 10],\ [73, 73, w^2 - w + 1],\ [83, 83, -4*w^3 + 5*w^2 + 17*w + 1],\ [83, 83, 3*w^3 - 3*w^2 - 14*w - 5],\ [89, 89, w^3 - w^2 - 4*w + 5],\ [89, 89, w^3 - 3*w^2 - w + 8],\ [97, 97, -w^3 + 7*w + 5],\ [97, 97, 2*w^3 - 3*w^2 - 7*w + 1],\ [103, 103, -3*w^3 + 8*w^2 + 7*w - 19],\ [113, 113, -w^2 + 2*w - 2],\ [125, 5, 2*w^3 - 5*w^2 - 3*w + 7],\ [127, 127, 2*w^2 - 3*w - 4],\ [137, 137, -w^3 + 3*w^2 + 3*w - 4],\ [137, 137, w^3 - w^2 - 6*w - 1],\ [149, 149, 2*w^3 - 3*w^2 - 5*w - 1],\ [151, 151, -w^3 + 3*w^2 - 5],\ [157, 157, -w^3 + 2*w^2 + w - 5],\ [163, 163, 4*w^3 - 4*w^2 - 18*w - 7],\ [167, 167, -3*w^3 + 4*w^2 + 13*w - 1],\ [167, 167, 2*w^2 - 4*w - 1],\ [173, 173, w^3 - 5*w - 1],\ [173, 173, 2*w^3 - 3*w^2 - 9*w + 1],\ [179, 179, -2*w^3 + 3*w^2 + 8*w - 4],\ [181, 181, 2*w^2 - 2*w - 5],\ [193, 193, 4*w^3 - 9*w^2 - 11*w + 17],\ [197, 197, w^3 - w^2 - 6*w + 1],\ [197, 197, -w^3 + 5*w^2 - w - 4],\ [199, 199, -3*w^3 + 4*w^2 + 11*w + 5],\ [211, 211, -2*w^3 + 5*w^2 + 6*w - 8],\ [227, 227, w^2 - 3*w - 5],\ [233, 233, 2*w^3 - 6*w^2 - 5*w + 16],\ [233, 233, -5*w^3 + 13*w^2 + 13*w - 26],\ [251, 251, -2*w^3 + 4*w^2 + 5*w - 4],\ [251, 251, -w^3 + 5*w^2 + w - 8],\ [251, 251, w^2 + w - 5],\ [251, 251, -w^3 + 2*w^2 + 3*w - 7],\ [257, 257, w^3 - 5*w^2 + 2*w + 11],\ [263, 263, -3*w^3 + 8*w^2 + 9*w - 17],\ [269, 269, -3*w^3 + 2*w^2 + 13*w + 7],\ [269, 269, 3*w^3 - 4*w^2 - 13*w - 1],\ [271, 271, 2*w^3 - 5*w^2 - 5*w + 7],\ [277, 277, -w^3 + w^2 + 5*w - 4],\ [283, 283, 3*w - 2],\ [293, 293, 3*w^3 - 2*w^2 - 15*w - 5],\ [307, 307, -w - 4],\ [307, 307, -2*w^3 + 11*w + 8],\ [313, 313, -2*w^3 + 2*w^2 + 7*w - 2],\ [347, 347, -w^3 + 3*w^2 + w - 10],\ [347, 347, 3*w^3 - 3*w^2 - 11*w - 4],\ [349, 349, -w^3 + w^2 + 4*w + 5],\ [349, 349, 2*w^2 - 2*w - 11],\ [353, 353, 2*w^3 - 7*w^2 - 3*w + 17],\ [353, 353, w^3 - w^2 - 6*w - 5],\ [359, 359, 2*w^2 - 4*w - 7],\ [359, 359, 3*w^2 - 3*w - 13],\ [361, 19, 6*w^3 - 6*w^2 - 28*w - 7],\ [361, 19, 2*w^2 - w - 8],\ [367, 367, -2*w^3 + w^2 + 9*w + 7],\ [367, 367, -4*w^3 + 5*w^2 + 16*w + 4],\ [373, 373, -2*w^3 + 3*w^2 + 6*w - 2],\ [373, 373, -w^3 + 3*w^2 + 3*w - 2],\ [373, 373, -2*w^3 + 7*w^2 + w - 13],\ [373, 373, 3*w^3 - 9*w^2 - 7*w + 22],\ [379, 379, -2*w^3 + 6*w^2 + 2*w - 11],\ [379, 379, 2*w^3 - 5*w^2 - 7*w + 7],\ [409, 409, -w^3 + 4*w^2 + 2*w - 14],\ [433, 433, -2*w^3 + 4*w^2 + 4*w - 5],\ [433, 433, 3*w^2 - 4*w - 10],\ [443, 443, -w^3 + 3*w^2 - 7],\ [443, 443, -w^3 + 3*w^2 + 4*w - 11],\ [457, 457, -3*w^3 + 5*w^2 + 10*w - 5],\ [461, 461, -2*w^3 + 3*w^2 + 8*w + 4],\ [463, 463, -5*w^3 + 3*w^2 + 25*w + 16],\ [479, 479, 3*w^2 - 6*w - 8],\ [487, 487, w^3 - 3*w^2 - 5*w + 8],\ [491, 491, 2*w^3 - 4*w^2 - 3*w + 2],\ [499, 499, w^3 - w^2 - 7*w + 4],\ [499, 499, w^3 - 6*w - 8],\ [521, 521, 2*w^3 - 4*w^2 - 8*w + 7],\ [521, 521, 3*w^3 - 5*w^2 - 8*w - 1],\ [521, 521, w^3 - 5*w + 1],\ [521, 521, w^3 - 8*w + 2],\ [523, 523, -2*w^3 + 5*w^2 + 4*w - 4],\ [547, 547, -2*w^3 + 4*w^2 + 6*w - 1],\ [547, 547, -w^3 - w^2 + 6*w + 11],\ [563, 563, -2*w^3 + 8*w^2 - 3*w - 8],\ [569, 569, 3*w^3 - 7*w^2 - 10*w + 13],\ [571, 571, -3*w^3 + 4*w^2 + 11*w - 1],\ [577, 577, -w^3 + 5*w^2 - 3*w - 10],\ [601, 601, -2*w^3 + 6*w^2 + 4*w - 17],\ [607, 607, 2*w^3 - 12*w - 5],\ [613, 613, 6*w^3 - 5*w^2 - 27*w - 11],\ [613, 613, 2*w + 5],\ [631, 631, 5*w^3 - 14*w^2 - 11*w + 29],\ [641, 641, w^3 + w^2 - 5*w - 8],\ [641, 641, -w^3 + 5*w^2 - 13],\ [643, 643, w^2 + w - 7],\ [643, 643, -3*w^3 + 3*w^2 + 15*w + 8],\ [661, 661, 3*w^3 - 2*w^2 - 14*w - 4],\ [691, 691, -2*w^3 + 3*w^2 + 9*w - 7],\ [691, 691, 2*w^3 - 5*w^2 - 3*w + 11],\ [709, 709, 7*w^3 - 16*w^2 - 20*w + 32],\ [709, 709, -w^3 + 4*w^2 + 2*w - 4],\ [709, 709, -2*w^3 + 3*w^2 + 4*w - 2],\ [719, 719, -2*w^3 + 3*w^2 + 7*w - 7],\ [719, 719, -w^3 + 4*w^2 - 14],\ [739, 739, 5*w^3 - 3*w^2 - 24*w - 17],\ [739, 739, -4*w^3 + 10*w^2 + 10*w - 17],\ [743, 743, 2*w^3 - 2*w^2 - 11*w - 2],\ [757, 757, -3*w^3 + 5*w^2 + 11*w - 2],\ [761, 761, w^3 - 3*w - 5],\ [761, 761, w^2 - 5*w - 1],\ [769, 769, -w^3 - w^2 + 9*w + 8],\ [773, 773, -2*w^3 + 4*w^2 + 7*w - 2],\ [797, 797, -2*w^3 + w^2 + 12*w + 10],\ [797, 797, -2*w^3 + 5*w^2 + 3*w + 1],\ [809, 809, 3*w^2 - 4*w - 8],\ [821, 821, -3*w^3 + 6*w^2 + 9*w - 5],\ [823, 823, -2*w^3 + 5*w^2 + w - 7],\ [823, 823, -3*w^3 + 6*w^2 + 6*w - 10],\ [827, 827, w^3 + 2*w^2 - 5*w - 7],\ [827, 827, w^3 - 2*w^2 - 6*w - 4],\ [829, 829, 3*w^3 - w^2 - 15*w - 14],\ [829, 829, w^3 + 2*w^2 - 7*w - 13],\ [839, 839, 4*w^3 - 11*w^2 - 8*w + 26],\ [853, 853, w^3 - 4*w - 8],\ [863, 863, 5*w^3 - 2*w^2 - 26*w - 14],\ [863, 863, 2*w^3 - 5*w^2 - 5*w + 5],\ [881, 881, 2*w^3 + w^2 - 11*w - 11],\ [883, 883, -6*w^3 + 15*w^2 + 14*w - 32],\ [883, 883, -w^3 + 2*w^2 + 2*w - 8],\ [887, 887, w^3 - w^2 - 7*w + 2],\ [907, 907, 3*w^3 - 3*w^2 - 10*w - 5],\ [907, 907, w^3 - 2*w^2 - 2*w - 4],\ [919, 919, 3*w^3 - 3*w^2 - 11*w - 2],\ [919, 919, -4*w^3 + 10*w^2 + 7*w - 16],\ [929, 929, 3*w^3 - 3*w^2 - 10*w + 1],\ [937, 937, 6*w^3 - 8*w^2 - 24*w + 1],\ [947, 947, 3*w^3 - 6*w^2 - 8*w + 8],\ [953, 953, 4*w - 1],\ [953, 953, 4*w^3 - 9*w^2 - 10*w + 16],\ [961, 31, -w^3 + 6*w - 2],\ [967, 967, 2*w^3 - 8*w - 7],\ [967, 967, 4*w^3 - 9*w^2 - 12*w + 14],\ [971, 971, 5*w^3 - 6*w^2 - 20*w - 4]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, 0, 1, 0, -4, 2, -8, -8, 8, 2, -6, -6, -10, -10, -2, -4, 2, -6, 4, 4, 6, 6, 18, 2, 4, -18, -2, 0, 10, -14, 6, 4, 10, 4, 0, 24, 6, -22, -8, -22, 6, 2, -22, 8, 12, -20, -10, -6, -28, 28, -20, -12, 10, 12, -18, -26, 20, 18, -12, -18, -32, 4, 14, -36, -20, 22, -18, 2, -6, 0, 12, 2, 30, -20, -8, 22, -18, -10, 18, 12, -12, 2, -26, -18, -12, -4, 2, -10, 16, 0, -32, -8, -8, -20, 10, -6, 18, -22, -4, -8, -4, -24, -6, 32, 34, 18, 8, -26, -10, -20, 18, -30, 36, 28, -42, -28, -32, -38, 34, 22, -40, -20, 20, 4, 24, 6, -6, 50, -30, -54, -22, -18, 10, -42, -24, -40, -28, -24, 46, 2, 36, 22, -8, -8, -38, -20, -52, 48, -12, 44, -28, 16, -30, 50, -36, 26, -54, 26, -8, 36, -52] 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 + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]