/* 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([-5, -8, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([9, 9, 2*w + 1]) primes_array = [ [2, 2, -w - 1],\ [3, 3, w + 2],\ [4, 2, w^2 - w - 7],\ [5, 5, w],\ [9, 3, -w^2 + 2*w + 4],\ [13, 13, -w + 2],\ [25, 5, w^2 - 8],\ [29, 29, 2*w + 3],\ [37, 37, w + 4],\ [37, 37, -3*w^2 + 2*w + 24],\ [37, 37, w^2 + 2*w - 2],\ [47, 47, w^2 - 2],\ [53, 53, w^2 - 2*w - 6],\ [61, 61, w^2 + 2*w + 2],\ [71, 71, 2*w - 1],\ [71, 71, -w^2 + 4*w + 2],\ [71, 71, -w^2 + 4*w - 2],\ [73, 73, -w^2 + 4*w + 4],\ [79, 79, -2*w + 7],\ [83, 83, -2*w^2 + 13],\ [89, 89, -3*w - 4],\ [97, 97, -4*w^2 + 2*w + 33],\ [101, 101, 2*w^2 - w - 12],\ [103, 103, 2*w^2 - 3*w - 4],\ [103, 103, 2*w^2 - 2*w - 11],\ [103, 103, w^2 - 2*w - 12],\ [109, 109, 2*w - 3],\ [113, 113, -2*w^2 + w + 18],\ [137, 137, 2*w^2 - 3*w - 12],\ [149, 149, -2*w^2 + 3*w + 18],\ [151, 151, -2*w^2 + 4*w + 9],\ [163, 163, 2*w^2 - 3*w - 6],\ [163, 163, -2*w^2 - w + 8],\ [163, 163, w - 6],\ [167, 167, w^2 - 12],\ [169, 13, w^2 + 2*w - 4],\ [173, 173, -w - 6],\ [179, 179, 2*w^2 + 3*w + 2],\ [193, 193, -4*w - 1],\ [199, 199, 3*w - 8],\ [211, 211, -4*w^2 + 2*w + 27],\ [211, 211, -6*w^2 + 4*w + 43],\ [211, 211, 3*w^2 - 4*w - 18],\ [223, 223, 2*w^2 - 2*w - 19],\ [227, 227, -3*w^2 + 28],\ [227, 227, -3*w^2 + 6*w + 4],\ [227, 227, -2*w^2 + 2*w + 1],\ [233, 233, -5*w - 2],\ [233, 233, -4*w - 7],\ [233, 233, -7*w^2 + 6*w + 48],\ [239, 239, -4*w^2 + 5*w + 24],\ [241, 241, 2*w^2 - 9],\ [257, 257, -7*w^2 + 4*w + 56],\ [257, 257, -2*w^2 + 3*w + 16],\ [257, 257, -3*w^2 + 2*w + 26],\ [263, 263, 2*w^2 - 5*w - 8],\ [269, 269, 2*w^2 - 6*w - 7],\ [271, 271, -6*w^2 + 5*w + 44],\ [271, 271, -2*w^2 - w + 2],\ [271, 271, 3*w - 2],\ [283, 283, 2*w^2 - 2*w - 7],\ [293, 293, -6*w^2 + 3*w + 46],\ [307, 307, -2*w^2 + 3],\ [307, 307, -4*w^2 + 6*w + 21],\ [307, 307, -4*w^2 + 9*w + 6],\ [311, 311, -4*w^2 + 39],\ [313, 313, -4*w^2 + 8*w + 9],\ [313, 313, -w^2 - 2*w - 4],\ [313, 313, 5*w^2 - 10*w - 18],\ [331, 331, -4*w^2 + 4*w + 29],\ [331, 331, 4*w^2 - w - 34],\ [331, 331, -3*w^2 + 8*w + 2],\ [337, 337, -8*w^2 + 6*w + 57],\ [337, 337, 4*w^2 - 4*w - 31],\ [337, 337, -3*w^2 + 2*w + 18],\ [343, 7, -7],\ [349, 349, 4*w^2 - 10*w - 11],\ [349, 349, w^2 - 6*w - 6],\ [349, 349, w^2 + 2*w - 14],\ [359, 359, -4*w^2 + 3*w + 26],\ [359, 359, 5*w + 6],\ [359, 359, 3*w - 4],\ [367, 367, 2*w^2 - 7],\ [379, 379, 2*w^2 + w - 4],\ [397, 397, 4*w - 11],\ [401, 401, 2*w - 9],\ [409, 409, w^2 - 4*w - 8],\ [421, 421, 7*w + 6],\ [443, 443, w - 8],\ [449, 449, -5*w^2 + 2*w + 38],\ [461, 461, 3*w^2 - 4*w - 6],\ [463, 463, -5*w - 8],\ [467, 467, 4*w^2 - 7*w - 8],\ [479, 479, w^2 - 14],\ [491, 491, w^2 - 6*w - 2],\ [499, 499, -5*w^2 + 8*w + 22],\ [521, 521, 2*w^2 + w - 14],\ [523, 523, -5*w^2 + 6*w + 28],\ [541, 541, 4*w^2 - 12*w - 11],\ [547, 547, 3*w^2 - 4*w - 24],\ [557, 557, 3*w^2 - 4*w - 12],\ [563, 563, 4*w^2 - 7*w - 14],\ [563, 563, -8*w^2 + 8*w + 53],\ [563, 563, -3*w^2 + 4*w + 22],\ [569, 569, -3*w^2 + 10*w + 6],\ [571, 571, -3*w^2 + 26],\ [571, 571, -7*w^2 + 6*w + 54],\ [571, 571, -4*w^2 + w + 32],\ [577, 577, -6*w^2 + 4*w + 49],\ [587, 587, -8*w^2 + 7*w + 54],\ [587, 587, -4*w^2 + 12*w + 3],\ [587, 587, 3*w^2 - 22],\ [593, 593, 6*w + 7],\ [599, 599, 4*w^2 - 4*w - 23],\ [601, 601, -w^2 - 4],\ [607, 607, -3*w^2 + 6*w + 14],\ [617, 617, 2*w^2 + w + 2],\ [619, 619, -6*w^2 + 6*w + 41],\ [643, 643, 2*w^2 - 3*w - 22],\ [653, 653, -2*w^2 - w + 16],\ [677, 677, 4*w - 3],\ [683, 683, 2*w^2 - 5*w - 22],\ [691, 691, 4*w^2 - 9*w - 14],\ [719, 719, -2*w^2 + 8*w - 7],\ [727, 727, 2*w^2 + 2*w + 3],\ [739, 739, 5*w^2 - 2*w - 32],\ [743, 743, 4*w^2 - 3*w - 24],\ [743, 743, -w^2 - 8*w - 8],\ [743, 743, 4*w - 9],\ [757, 757, -6*w - 11],\ [769, 769, w^2 - 6*w - 8],\ [797, 797, -3*w^2 - 4*w + 2],\ [797, 797, -2*w^2 + 2*w - 1],\ [797, 797, -12*w^2 + 9*w + 86],\ [811, 811, -5*w^2 + 2*w + 44],\ [823, 823, -3*w^2 + 6*w + 2],\ [827, 827, -w^2 + 6*w - 6],\ [829, 829, 2*w^2 + 5*w + 6],\ [839, 839, -2*w^2 + 6*w - 3],\ [841, 29, 4*w^2 - 6*w - 23],\ [853, 853, -6*w^2 + 17*w + 12],\ [857, 857, 3*w^2 - 2*w - 14],\ [859, 859, -13*w^2 + 8*w + 102],\ [863, 863, -2*w^2 - 2*w + 27],\ [881, 881, 4*w^2 - 11*w - 12],\ [907, 907, 4*w^2 - 10*w - 13],\ [919, 919, -9*w^2 + 6*w + 64],\ [929, 929, -6*w^2 + 2*w + 53],\ [937, 937, 3*w^2 - 2*w - 6],\ [941, 941, 4*w^2 - 21],\ [991, 991, -6*w^2 + 7*w + 34]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 0, -3, 2, -6, -6, -6, -2, -6, 6, -6, 8, 6, -6, -8, 0, -8, -6, 0, -4, -6, -10, 6, 0, 0, 0, 18, 6, -18, 6, -8, -12, -12, 12, 24, -18, 2, 20, 18, 0, -4, 12, -12, -8, 12, 12, 12, 26, 22, -6, 24, -26, -18, -14, 2, -8, 10, -24, 24, 16, -12, 6, 12, 12, 20, 24, 10, 6, 30, -28, -12, 12, -18, -30, -18, 16, 30, 10, 18, -8, -16, 0, 24, -36, -18, -10, 6, -6, 4, -2, 2, 0, 36, -40, 4, -4, -10, -36, 30, -36, -2, 36, 44, -20, 22, -12, -12, 4, 18, -12, 12, -12, 6, -24, -42, -32, -18, 12, -12, -30, 2, -12, 12, 32, 24, 36, 48, 8, 40, 6, -18, 2, -2, 30, 36, 0, 12, -18, 0, 30, -6, -38, -36, 24, -30, 12, 56, 50, 6, 42, -48] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, w + 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]