/* 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, 8, 0, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([32, 32, w^4 + w^3 - 5*w^2 - 4*w + 5]) primes_array = [ [2, 2, w^2 - 3],\ [11, 11, -w^4 + 5*w^2 + w - 4],\ [13, 13, -w^3 + w^2 + 3*w - 4],\ [16, 2, w^4 - w^3 - 3*w^2 + 3*w - 1],\ [17, 17, w^4 - 4*w^2 + 2],\ [31, 31, w^4 - 4*w^2 - w + 3],\ [43, 43, -w^3 + 4*w - 2],\ [53, 53, w^4 - 3*w^2 - 1],\ [53, 53, w^4 - w^3 - 4*w^2 + 2*w + 1],\ [53, 53, -w^3 - w^2 + 3*w + 4],\ [61, 61, -w^3 + w^2 + 5*w - 2],\ [61, 61, w^4 - 4*w^2 + w + 1],\ [61, 61, w^3 + w^2 - 4*w - 3],\ [67, 67, -2*w^3 + w^2 + 6*w - 2],\ [71, 71, -2*w^3 + w^2 + 7*w - 3],\ [71, 71, 2*w^4 - 4*w^3 - 7*w^2 + 13*w - 1],\ [73, 73, -w^4 + 2*w^3 + 3*w^2 - 7*w],\ [73, 73, w^4 + w^3 - 3*w^2 - 4*w - 2],\ [79, 79, w^4 - w^3 - 5*w^2 + 4*w + 6],\ [83, 83, -2*w^4 + w^3 + 9*w^2 - 3*w - 6],\ [97, 97, w^4 - w^3 - 2*w^2 + 4*w - 3],\ [103, 103, -w^3 - w^2 + 2*w + 3],\ [103, 103, w^4 - 2*w^3 - 4*w^2 + 5*w + 3],\ [107, 107, -w^4 - w^3 + 6*w^2 + 3*w - 6],\ [113, 113, -w^4 + 2*w^3 + 4*w^2 - 6*w - 2],\ [127, 127, w^4 + 2*w^3 - 5*w^2 - 7*w + 4],\ [137, 137, -2*w - 1],\ [139, 139, -2*w^4 + 2*w^3 + 8*w^2 - 6*w - 1],\ [151, 151, 2*w^4 - 8*w^2 - w + 2],\ [157, 157, w^4 - 3*w^3 - 2*w^2 + 10*w - 3],\ [157, 157, -2*w^4 + 2*w^3 + 7*w^2 - 5*w + 1],\ [163, 163, w^4 - 2*w^3 - 3*w^2 + 6*w - 3],\ [163, 163, w^4 + w^3 - 6*w^2 - 4*w + 5],\ [163, 163, -w^3 - w^2 + 4*w + 1],\ [167, 167, -w^4 + 2*w^2 + 2],\ [167, 167, -w^4 - w^3 + 4*w^2 + 4*w - 3],\ [169, 13, -w^3 + 2*w^2 + 2*w - 2],\ [169, 13, w^2 + w - 5],\ [173, 173, w^4 + w^3 - 4*w^2 - 2*w + 1],\ [173, 173, -w^3 + w^2 + w - 2],\ [179, 179, -2*w^2 - w + 2],\ [191, 191, w^4 - w^3 - 5*w^2 + 4*w],\ [193, 193, w^3 - 2*w - 2],\ [193, 193, w^4 - 5*w^2 + 1],\ [197, 197, -2*w^4 + 3*w^3 + 6*w^2 - 8*w + 2],\ [199, 199, w^4 - 3*w^2 + w - 2],\ [223, 223, -2*w^4 + 2*w^3 + 8*w^2 - 5*w - 4],\ [227, 227, -w^3 - w^2 + 5*w + 4],\ [229, 229, -w^3 - 3*w^2 + w + 4],\ [239, 239, w^2 - 2*w - 2],\ [239, 239, 2*w^2 - w - 4],\ [243, 3, -3],\ [257, 257, -w^4 + 6*w^2 + w - 5],\ [263, 263, -w^4 + 5*w^2 + 2*w - 5],\ [269, 269, w^4 - 5*w^2 + 2*w + 1],\ [269, 269, w^3 + 2*w^2 - 4*w - 6],\ [269, 269, w^3 - 3*w^2 - 4*w + 7],\ [271, 271, -2*w^3 + 2*w^2 + 8*w - 5],\ [271, 271, -w^4 + w^3 + 4*w^2 - 5*w - 2],\ [277, 277, -2*w^4 + w^3 + 7*w^2 - 2*w - 1],\ [281, 281, -w^3 + w^2 + 2*w - 5],\ [293, 293, 2*w^4 - 9*w^2 - w + 7],\ [307, 307, -3*w^3 + 2*w^2 + 10*w - 4],\ [307, 307, 2*w^4 + 2*w^3 - 11*w^2 - 7*w + 11],\ [317, 317, w^3 - 2*w^2 - 5*w + 3],\ [337, 337, -w^4 - 2*w^3 + 5*w^2 + 8*w - 5],\ [347, 347, -w^4 + w^3 + 3*w^2 - 4*w - 2],\ [347, 347, -w^4 - 2*w^3 + 6*w^2 + 6*w - 6],\ [353, 353, -w^4 - w^3 + 2*w^2 + 5*w + 6],\ [353, 353, 2*w^4 - w^3 - 8*w^2 + 3*w + 5],\ [361, 19, w^3 - 6*w + 2],\ [383, 383, w^4 - 3*w^3 - 4*w^2 + 10*w + 1],\ [383, 383, -w^4 - 2*w^3 + 5*w^2 + 6*w - 3],\ [383, 383, w^2 - 6],\ [389, 389, -w^4 - 3*w^3 + 6*w^2 + 12*w - 3],\ [397, 397, -2*w^4 + w^3 + 7*w^2 - w - 4],\ [401, 401, w^4 - 2*w^2 - 3*w - 5],\ [401, 401, -w^3 + 2*w^2 + 5*w - 9],\ [409, 409, 2*w^4 - 9*w^2 + 4],\ [419, 419, w^4 - w^3 - 2*w^2 + 3*w - 4],\ [421, 421, 2*w^4 - w^3 - 10*w^2 + 2*w + 8],\ [421, 421, -2*w^4 + w^3 + 11*w^2 - 3*w - 10],\ [431, 431, w^2 - 2*w - 4],\ [439, 439, -2*w^4 + w^3 + 8*w^2 - w - 3],\ [449, 449, w^4 + w^3 - 5*w^2 - 2*w + 4],\ [457, 457, 2*w^4 + w^3 - 7*w^2 - 3*w + 2],\ [457, 457, -4*w^4 + 5*w^3 + 14*w^2 - 17*w + 1],\ [461, 461, w^4 + 3*w^3 - 5*w^2 - 10*w],\ [463, 463, w^4 - 4*w^2 + 3*w + 1],\ [479, 479, 2*w^4 - 7*w^2 + w - 1],\ [499, 499, -2*w^4 + 3*w^3 + 7*w^2 - 7*w - 2],\ [503, 503, w^4 + 2*w^3 - 7*w^2 - 8*w + 9],\ [509, 509, 3*w^3 - w^2 - 10*w + 3],\ [541, 541, w^4 - 6*w^2 - 3*w + 5],\ [557, 557, 2*w^4 - w^3 - 6*w^2 + 4*w - 4],\ [569, 569, 2*w^3 - 2*w^2 - 8*w + 3],\ [601, 601, -2*w^4 + w^3 + 7*w^2 - 3*w - 2],\ [619, 619, -w^4 + 2*w^3 + 6*w^2 - 7*w - 3],\ [619, 619, 2*w^4 + 2*w^3 - 10*w^2 - 7*w + 8],\ [631, 631, -w^4 + 2*w^3 + 3*w^2 - 8*w - 1],\ [641, 641, -2*w^4 + w^3 + 9*w^2 - 3*w - 10],\ [641, 641, -w^4 + 2*w^2 + 2*w + 2],\ [643, 643, w^4 + w^3 - 5*w^2 - 2*w + 2],\ [647, 647, 3*w^4 - 2*w^3 - 11*w^2 + 4*w + 1],\ [647, 647, -w^4 - 2*w^3 + 2*w^2 + 5*w + 3],\ [653, 653, w^4 + w^3 - 2*w^2 - 4*w - 5],\ [653, 653, w^4 - w^3 - 3*w^2 + 2*w - 4],\ [659, 659, w^4 + w^3 - 8*w^2 - 5*w + 10],\ [661, 661, -w^4 + 2*w^3 + w^2 - 7*w + 2],\ [661, 661, -w^4 + 3*w^2 - w - 4],\ [673, 673, -3*w^4 + 2*w^3 + 13*w^2 - 6*w - 9],\ [673, 673, -2*w^3 + w^2 + 9*w + 1],\ [677, 677, -2*w^4 + 8*w^2 - 5],\ [701, 701, 2*w^4 - 7*w^2 + 2],\ [709, 709, 2*w^4 - w^3 - 7*w^2 - 1],\ [727, 727, 3*w^4 - 2*w^3 - 10*w^2 + 5*w - 1],\ [733, 733, 2*w^4 - 3*w^3 - 9*w^2 + 8*w + 5],\ [739, 739, -2*w^4 - w^3 + 8*w^2 + 4*w - 6],\ [751, 751, 2*w^4 + w^3 - 8*w^2 - 6*w + 4],\ [751, 751, -2*w^4 + 2*w^3 + 8*w^2 - 5*w - 2],\ [757, 757, -2*w^4 + w^3 + 9*w^2 - 5*w - 2],\ [757, 757, 2*w^4 - 2*w^3 - 6*w^2 + 7*w - 4],\ [761, 761, 4*w^3 - w^2 - 14*w],\ [761, 761, -2*w^4 + w^3 + 9*w^2 - w - 6],\ [787, 787, 2*w^4 + 2*w^3 - 7*w^2 - 7*w + 3],\ [797, 797, w^4 - 4*w^3 - 3*w^2 + 12*w - 3],\ [809, 809, -w^4 + 6*w^2 - 2*w - 2],\ [811, 811, -w^4 - 2*w^3 + 3*w^2 + 7*w - 2],\ [821, 821, w^4 - w^3 - 4*w^2 + 3*w + 6],\ [823, 823, 3*w^3 - 8*w - 2],\ [827, 827, 2*w^3 - w^2 - 10*w + 2],\ [839, 839, -w^3 + 5*w + 5],\ [839, 839, w^4 + 3*w^3 - 5*w^2 - 10*w + 6],\ [839, 839, 2*w^4 - 8*w^2 + w + 2],\ [841, 29, w^4 - 5*w^2 - 2*w - 1],\ [853, 853, 3*w^4 - 2*w^3 - 11*w^2 + 4*w + 3],\ [859, 859, 2*w^4 - 3*w^3 - 8*w^2 + 8*w],\ [863, 863, -2*w^4 + w^3 + 9*w^2 - 4*w - 1],\ [863, 863, -2*w^3 - 2*w^2 + 5*w + 6],\ [881, 881, -w^4 + w^3 + 6*w^2 - 5*w - 2],\ [881, 881, -3*w^4 + 5*w^3 + 10*w^2 - 18*w + 1],\ [883, 883, -2*w^3 - w^2 + 9*w + 5],\ [883, 883, -4*w^3 + 2*w^2 + 12*w - 3],\ [887, 887, 4*w^3 - w^2 - 14*w + 4],\ [907, 907, 2*w^4 - 3*w^3 - 5*w^2 + 9*w - 4],\ [911, 911, -w^4 + 2*w^3 + 2*w^2 - 8*w],\ [919, 919, -w^4 + w^3 + 5*w^2 - 6*w - 2],\ [929, 929, -w^4 + 6*w^2 - 4],\ [937, 937, -w^4 + 3*w^3 + 2*w^2 - 9*w + 6],\ [947, 947, 3*w^3 - w^2 - 9*w + 4],\ [961, 31, -2*w^4 + 5*w^3 + 6*w^2 - 16*w + 4],\ [961, 31, w^4 - 3*w^3 - 4*w^2 + 12*w - 3],\ [971, 971, 4*w^3 - 3*w^2 - 14*w + 6],\ [983, 983, w^4 + 2*w^3 - 3*w^2 - 7*w - 4],\ [983, 983, -w^4 + w^3 + 4*w^2 - 6*w - 1],\ [983, 983, -2*w^4 - w^3 + 11*w^2 + 4*w - 9],\ [983, 983, 2*w^4 + 2*w^3 - 11*w^2 - 7*w + 9],\ [997, 997, w^4 - 3*w^3 - 6*w^2 + 10*w + 7]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 2, 4, -3, -4, 8, -8, 6, -12, 6, 6, 0, 4, 2, -8, 10, 6, -2, 4, -4, 8, -2, 2, 16, -2, 18, 6, -16, -16, -10, 2, 2, 2, -20, 18, 18, -6, 22, 10, 18, 8, 8, -16, -22, -18, -12, 20, 12, 22, 16, 4, -16, 26, 8, -14, 10, -10, -8, -20, 2, 20, 18, 0, -28, 14, -22, -36, 8, 30, 22, -30, 8, 8, 16, -18, 26, 2, 6, -12, 12, 10, 8, -32, -10, -32, 22, -2, 38, 0, -24, -4, 0, 24, 14, 32, 0, -28, -36, -32, 4, -2, -2, -20, 20, 24, -34, -6, -44, -36, -18, -6, -36, -18, -6, -28, 40, 20, 36, -50, 2, 10, 22, -6, -14, -8, 16, 30, 4, 10, 26, -22, 12, 2, -24, 40, -30, 22, 56, 4, 6, 6, 40, -34, -20, -36, 16, 38, -18, -8, -24, -18, -38, 36, 48, -18, 14, 8, 10] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]