/* 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([8, -10, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([8,8,1/2*w^2 + 3/2*w - 2]) primes_array = [ [2, 2, 1/2*w^2 - 1/2*w - 4],\ [2, 2, 1/2*w^2 + 1/2*w - 3],\ [2, 2, -w + 1],\ [23, 23, -w^2 + w + 7],\ [23, 23, w^2 + w - 7],\ [23, 23, -2*w + 1],\ [27, 3, 3],\ [29, 29, -w^2 - 3*w + 1],\ [29, 29, w^2 - 3*w + 1],\ [29, 29, -2*w^2 + 21],\ [31, 31, -3*w^2 + w + 31],\ [47, 47, 2*w - 3],\ [47, 47, w^2 + w - 5],\ [47, 47, w^2 - w - 9],\ [61, 61, w^2 - w - 11],\ [61, 61, -w^2 - w + 3],\ [61, 61, -2*w + 5],\ [89, 89, w^2 - w - 1],\ [89, 89, w^2 + w - 13],\ [89, 89, -2*w - 5],\ [97, 97, 2*w + 7],\ [97, 97, -w^2 + w - 1],\ [97, 97, -w^2 - w + 15],\ [101, 101, -2*w - 1],\ [101, 101, w^2 - w - 5],\ [101, 101, w^2 + w - 9],\ [109, 109, w^2 + 3*w + 1],\ [109, 109, -2*w^2 + 23],\ [109, 109, -w^2 + 3*w - 3],\ [125, 5, -5],\ [139, 139, -2*w - 3],\ [139, 139, w^2 + w - 11],\ [139, 139, w^2 - w - 3],\ [151, 151, w^2 + 3*w - 5],\ [151, 151, 2*w^2 - 17],\ [151, 151, w^2 - 3*w - 3],\ [157, 157, 4*w^2 - 39],\ [157, 157, 5*w^2 - w - 49],\ [157, 157, -2*w^2 + 6*w + 1],\ [163, 163, 3*w^2 - w - 33],\ [163, 163, w^2 - 5*w + 7],\ [163, 163, 2*w^2 + 4*w - 3],\ [233, 233, -5*w^2 + w + 53],\ [233, 233, -2*w^2 + 8*w - 7],\ [233, 233, -2*w^2 + 6*w + 3],\ [263, 263, 2*w^2 + 2*w - 11],\ [263, 263, 2*w^2 - 2*w - 17],\ [263, 263, 4*w - 5],\ [271, 271, w^2 + w + 1],\ [271, 271, w^2 - w - 15],\ [271, 271, -2*w + 9],\ [277, 277, w^2 - 5*w + 1],\ [277, 277, -3*w^2 + w + 27],\ [277, 277, 2*w^2 + 4*w - 9],\ [281, 281, 2*w^2 - 2*w + 1],\ [281, 281, -w^2 - 5*w - 5],\ [281, 281, 4*w + 13],\ [283, 283, -2*w^2 - 6*w + 3],\ [283, 283, 2*w^2 - 6*w + 1],\ [283, 283, -4*w^2 + 41],\ [311, 311, 4*w^2 - 2*w - 43],\ [311, 311, w^2 - 7*w + 11],\ [311, 311, 3*w^2 + 5*w - 7],\ [337, 337, 3*w^2 + w - 27],\ [337, 337, -w^2 - 5*w + 3],\ [337, 337, -2*w^2 + 4*w + 7],\ [343, 7, -7],\ [349, 349, 2*w^2 + 2*w - 15],\ [349, 349, -4*w + 1],\ [349, 349, 2*w^2 - 2*w - 13],\ [373, 373, w^2 - 3*w - 5],\ [373, 373, 2*w^2 - 15],\ [373, 373, w^2 + 3*w - 7],\ [401, 401, 2*w^2 - 2*w - 23],\ [401, 401, -4*w + 11],\ [401, 401, -2*w^2 - 2*w + 5],\ [419, 419, -w^2 + 7*w - 7],\ [419, 419, -4*w^2 + 2*w + 39],\ [419, 419, -3*w^2 - 5*w + 11],\ [433, 433, -4*w^2 + 4*w + 31],\ [433, 433, -4*w^2 - 4*w + 25],\ [433, 433, -3*w^2 - w + 37],\ [449, 449, -4*w^2 + 45],\ [449, 449, 2*w^2 + 6*w + 1],\ [449, 449, -2*w^2 + 6*w - 5],\ [457, 457, 4*w + 11],\ [457, 457, 2*w^2 - 2*w - 1],\ [457, 457, -2*w^2 - 2*w + 27],\ [461, 461, 2*w^2 + 2*w - 9],\ [461, 461, 4*w - 7],\ [461, 461, 2*w^2 - 2*w - 19],\ [463, 463, -w^2 + 3*w - 5],\ [463, 463, -2*w^2 + 25],\ [463, 463, -w^2 - 3*w - 3],\ [467, 467, w^2 + w - 17],\ [467, 467, -w^2 + w - 3],\ [467, 467, -2*w - 9],\ [523, 523, 2*w^2 - 2*w - 21],\ [523, 523, -2*w^2 - 2*w + 7],\ [523, 523, 4*w - 9],\ [557, 557, -4*w^2 - 8*w + 15],\ [557, 557, 2*w^2 - 10*w + 5],\ [557, 557, -6*w^2 + 2*w + 57],\ [587, 587, 5*w^2 + 13*w - 9],\ [587, 587, -4*w^2 + 14*w - 7],\ [587, 587, 9*w^2 - w - 93],\ [593, 593, 4*w^2 - 2*w - 35],\ [593, 593, w^2 - 7*w + 3],\ [593, 593, -3*w^2 - 5*w + 15],\ [619, 619, 2*w^2 - 13],\ [619, 619, w^2 + 3*w - 9],\ [619, 619, w^2 - 3*w - 7],\ [643, 643, 3*w^2 + w - 23],\ [643, 643, w^2 + 5*w - 7],\ [643, 643, 2*w^2 - 4*w - 11],\ [647, 647, w^2 + 5*w - 1],\ [647, 647, 2*w^2 - 4*w - 5],\ [647, 647, 3*w^2 + w - 29],\ [653, 653, 2*w^2 + 4*w - 1],\ [653, 653, 3*w^2 - w - 35],\ [653, 653, w^2 - 5*w + 9],\ [659, 659, -2*w^2 + 8*w - 1],\ [659, 659, -3*w^2 - 7*w + 11],\ [659, 659, 5*w^2 - w - 47],\ [683, 683, 2*w^2 + 4*w - 11],\ [683, 683, 3*w^2 - w - 25],\ [683, 683, w^2 - 5*w - 1],\ [709, 709, 7*w^2 + 17*w - 19],\ [709, 709, -2*w^2 + 10*w - 13],\ [709, 709, 9*w^2 - w - 91],\ [743, 743, 3*w^2 + 3*w - 17],\ [743, 743, 3*w^2 - 3*w - 25],\ [743, 743, 6*w - 7],\ [773, 773, -2*w^2 + 4*w + 3],\ [773, 773, 3*w^2 + w - 31],\ [773, 773, w^2 + 5*w + 1],\ [821, 821, -8*w + 5],\ [821, 821, -4*w^2 + 4*w + 29],\ [821, 821, -4*w^2 - 4*w + 27],\ [829, 829, -6*w^2 + 4*w + 53],\ [829, 829, -4*w^2 - 2*w + 51],\ [829, 829, 4*w^2 + 2*w - 49],\ [839, 839, -2*w^2 - 6*w + 9],\ [839, 839, -2*w^2 + 6*w + 5],\ [839, 839, 4*w^2 - 35],\ [853, 853, -5*w^2 + 5*w + 37],\ [853, 853, -5*w^2 - 5*w + 33],\ [853, 853, -5*w^2 + 3*w + 43],\ [883, 883, 2*w^2 - 5],\ [883, 883, w^2 - 3*w - 15],\ [883, 883, w^2 + 3*w - 17],\ [907, 907, -5*w^2 + w + 55],\ [907, 907, -3*w^2 - 7*w + 3],\ [907, 907, -2*w^2 + 8*w - 9],\ [929, 929, 2*w^2 - 2*w - 9],\ [929, 929, -4*w - 3],\ [929, 929, 2*w^2 + 2*w - 19],\ [953, 953, -2*w^2 + 12*w - 19],\ [953, 953, 7*w^2 - 3*w - 77],\ [953, 953, 5*w^2 + 9*w - 9],\ [977, 977, -3*w^2 + 11*w - 1],\ [977, 977, -4*w^2 - 10*w + 13],\ [977, 977, 7*w^2 - w - 67],\ [991, 991, w^2 - 3*w - 11],\ [991, 991, 2*w^2 - 9],\ [991, 991, w^2 + 3*w - 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -1, 1, 0, 0, -8, 4, 2, -6, 6, 0, -8, -8, -8, 2, 2, -10, -6, 6, -2, -2, -18, 10, 10, 14, -6, -14, 2, -18, 14, -12, -12, 4, 16, 8, 0, -22, 14, 2, 4, 4, -12, -18, -26, -6, 0, -32, 0, -24, 8, 8, -22, 10, -26, 10, -6, -6, 4, 4, 28, 16, -8, 24, -30, -14, 2, 8, 10, 22, -14, -10, 22, -26, 10, 30, -18, -28, -28, 4, 10, -18, -26, -30, 18, -14, -22, 38, 38, 18, -22, -18, 16, 32, -40, -36, 28, 12, -44, 20, -20, 10, 30, -14, -44, 44, 28, -30, -30, -14, 20, 44, -4, -36, -36, -12, 8, 24, 8, -30, -34, -30, -20, 36, 36, 4, 20, 36, -26, 38, -26, -48, -24, 24, 38, -10, 6, -10, -6, 10, -38, 34, 14, 0, 40, -56, -2, -22, 26, -36, 20, -44, 4, -4, 44, 14, 50, 14, 6, -18, 18, 30, -38, 14, 40, 32, -8] 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]