/* 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([7, 6, -5, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([7,7,-w + 1]) primes_array = [ [4, 2, -w^2 + w + 3],\ [7, 7, w],\ [7, 7, -w^2 + 2*w + 1],\ [7, 7, w^2 - 2],\ [7, 7, w - 1],\ [23, 23, -w^3 + w^2 + 3*w - 1],\ [23, 23, w^3 - 2*w^2 - 2*w + 2],\ [31, 31, w^2 - 5],\ [31, 31, -w^2 + 2*w + 4],\ [41, 41, -w^3 + 2*w^2 + 2*w - 6],\ [41, 41, w^3 - w^2 - 3*w - 3],\ [47, 47, w^2 - 2*w - 5],\ [47, 47, w^2 - 6],\ [71, 71, -w^3 + 2*w^2 + 3*w - 1],\ [71, 71, -w^3 + w^2 + 4*w - 3],\ [79, 79, -w - 3],\ [79, 79, w - 4],\ [81, 3, -3],\ [89, 89, w^2 - 3*w - 2],\ [89, 89, w^2 + w - 4],\ [97, 97, 2*w^3 - 5*w^2 - 4*w + 9],\ [97, 97, -2*w^3 + w^2 + 8*w + 2],\ [113, 113, w^3 - 2*w^2 - 4*w + 2],\ [113, 113, w^3 - w^2 - 5*w + 3],\ [121, 11, 2*w^2 - w - 9],\ [121, 11, -2*w^2 + 3*w + 8],\ [127, 127, w^3 - 3*w^2 - 2*w + 5],\ [127, 127, w^3 - 5*w - 1],\ [137, 137, 2*w - 1],\ [167, 167, 2*w^3 - 2*w^2 - 7*w - 2],\ [167, 167, w^3 - 7*w - 4],\ [167, 167, 2*w^3 - w^2 - 9*w - 2],\ [167, 167, 2*w^3 - 4*w^2 - 5*w + 9],\ [191, 191, 2*w^3 - 4*w^2 - 5*w + 5],\ [191, 191, -2*w^3 + 2*w^2 + 7*w - 2],\ [193, 193, -2*w^3 + 3*w^2 + 6*w - 6],\ [193, 193, -2*w^3 + 2*w^2 + 7*w - 4],\ [193, 193, -2*w^3 + 4*w^2 + 5*w - 3],\ [193, 193, 2*w^3 - 3*w^2 - 6*w + 1],\ [199, 199, -w^3 - 2*w^2 + 6*w + 10],\ [199, 199, -w^3 + 5*w^2 - w - 13],\ [223, 223, -w^3 + 2*w^2 + 3*w - 8],\ [223, 223, w^3 - w^2 - 4*w - 4],\ [233, 233, -w^2 - 1],\ [233, 233, w^2 - 2*w + 2],\ [239, 239, 3*w^2 - 2*w - 13],\ [239, 239, 3*w^2 - 4*w - 12],\ [241, 241, w^3 - w^2 - 6*w + 3],\ [241, 241, w^3 - 2*w^2 - 5*w + 3],\ [257, 257, -w^3 + 3*w^2 + 4*w - 9],\ [257, 257, -2*w^3 + 4*w^2 + 8*w - 11],\ [257, 257, -w^3 + 2*w^2 + 4],\ [257, 257, w^3 - 7*w - 3],\ [263, 263, -w^3 + w^2 + 3*w + 5],\ [263, 263, w^3 - 5*w^2 + 12],\ [263, 263, -w^3 - 2*w^2 + 7*w + 8],\ [263, 263, -w^3 + 7*w + 2],\ [271, 271, -w^3 + 3*w^2 + 2*w - 3],\ [271, 271, w^3 - 5*w + 1],\ [289, 17, 3*w^2 - 3*w - 8],\ [289, 17, 3*w^2 - 3*w - 10],\ [311, 311, -2*w^3 + 2*w^2 + 7*w - 1],\ [311, 311, -w^3 + 5*w^2 - w - 11],\ [311, 311, w^3 + 2*w^2 - 6*w - 8],\ [311, 311, -2*w^3 + 4*w^2 + 5*w - 6],\ [337, 337, w^3 - w^2 - 2*w - 4],\ [337, 337, 2*w^3 - 9*w - 4],\ [337, 337, 2*w^3 - 6*w^2 - 3*w + 11],\ [337, 337, -w^3 + 2*w^2 + w - 6],\ [353, 353, -w^3 + 4*w^2 - 12],\ [353, 353, w^3 + w^2 - 5*w - 9],\ [359, 359, 2*w^3 - 4*w^2 - 6*w + 5],\ [359, 359, 2*w^3 - 2*w^2 - 8*w + 3],\ [361, 19, -w^3 + 5*w^2 - 13],\ [361, 19, w^3 + 2*w^2 - 7*w - 9],\ [367, 367, 2*w^3 - 10*w - 5],\ [367, 367, w^3 - w^2 - 6*w + 2],\ [367, 367, -w^3 + 2*w^2 + 5*w - 4],\ [367, 367, 2*w^3 - 6*w^2 - 4*w + 13],\ [401, 401, -w^3 + 2*w^2 + 5*w - 5],\ [401, 401, -w^3 + w^2 + 6*w - 1],\ [409, 409, 2*w^3 - 3*w^2 - 6*w + 4],\ [409, 409, 3*w^3 - 3*w^2 - 12*w + 1],\ [409, 409, -3*w^3 + 6*w^2 + 9*w - 11],\ [409, 409, -2*w^3 + 3*w^2 + 6*w - 3],\ [431, 431, 3*w^2 - 5*w - 10],\ [431, 431, w^3 + w^2 - 8*w - 3],\ [457, 457, -2*w^3 + 4*w^2 + 4*w - 5],\ [457, 457, -2*w^3 + 2*w^2 + 6*w - 1],\ [463, 463, -2*w^3 + 7*w^2 + w - 16],\ [463, 463, 3*w^3 - 6*w^2 - 8*w + 8],\ [503, 503, -w^3 + 3*w^2 + 2*w - 12],\ [503, 503, -w^3 + 4*w^2 + 4*w - 10],\ [521, 521, w^3 + w^2 - 6*w - 2],\ [521, 521, -w^3 + 4*w^2 + w - 6],\ [529, 23, w^2 - w - 8],\ [569, 569, w^3 - 3*w - 6],\ [569, 569, -w^3 + 3*w^2 - 8],\ [577, 577, -w^3 + 4*w^2 - w - 10],\ [577, 577, w^3 + w^2 - 4*w - 8],\ [593, 593, -w^3 + 3*w^2 - 12],\ [593, 593, w^3 - 3*w - 10],\ [599, 599, w^3 + 3*w^2 - 7*w - 9],\ [599, 599, -w^3 + 3*w^2 + 3*w - 13],\ [601, 601, w^2 + 2*w - 4],\ [601, 601, w^2 - 4*w - 1],\ [607, 607, 2*w^2 - 13],\ [607, 607, w^3 + 2*w^2 - 7*w - 5],\ [607, 607, 2*w^3 - 3*w^2 - 8*w + 8],\ [607, 607, 2*w^2 - 4*w - 11],\ [617, 617, w^3 + w^2 - 9*w - 1],\ [617, 617, w^3 - w^2 - 4*w - 5],\ [617, 617, -w^3 + 2*w^2 + 3*w - 9],\ [617, 617, -w^3 + 4*w^2 + 4*w - 8],\ [625, 5, -5],\ [631, 631, -w^3 + 5*w^2 - 2*w - 13],\ [631, 631, w^3 + 2*w^2 - 5*w - 11],\ [641, 641, w^2 - 2*w + 3],\ [641, 641, -w^3 + 6*w - 2],\ [641, 641, -w^3 + 3*w^2 + 3*w - 3],\ [641, 641, -w^2 - 2],\ [647, 647, -2*w^3 + 5*w^2 + 4*w - 6],\ [647, 647, 2*w^3 - 4*w^2 - 5*w - 1],\ [647, 647, 3*w^3 - 7*w^2 - 7*w + 13],\ [647, 647, -2*w^3 + w^2 + 8*w - 1],\ [673, 673, -w^3 + 7*w - 2],\ [673, 673, -w^3 + 3*w^2 + 4*w - 4],\ [719, 719, -2*w^3 + 5*w^2 + 3*w - 12],\ [719, 719, 4*w^2 - 5*w - 10],\ [719, 719, -4*w^2 + 3*w + 11],\ [719, 719, 2*w^3 - w^2 - 7*w - 6],\ [727, 727, -w - 5],\ [727, 727, w - 6],\ [743, 743, w^2 + 2*w - 11],\ [743, 743, w^3 + 4*w^2 - 11*w - 11],\ [751, 751, -2*w^2 + w + 13],\ [751, 751, 2*w^2 - 3*w - 12],\ [769, 769, 2*w^3 - 6*w^2 - 3*w + 17],\ [769, 769, 3*w^3 - 2*w^2 - 11*w + 2],\ [809, 809, w^3 + 3*w^2 - 6*w - 11],\ [809, 809, -3*w^3 + 5*w^2 + 8*w - 11],\ [823, 823, -w^3 + w^2 + 2*w - 6],\ [823, 823, 4*w^2 - 5*w - 11],\ [823, 823, -4*w^2 + 3*w + 12],\ [823, 823, -w^3 + 4*w^2 + 4*w - 12],\ [839, 839, -2*w^3 + w^2 + 6*w + 5],\ [839, 839, -3*w^3 + 8*w^2 + 7*w - 17],\ [839, 839, 3*w^3 - w^2 - 14*w - 5],\ [839, 839, -2*w^3 + 5*w^2 + 2*w - 10],\ [857, 857, w^3 + w^2 - 8*w - 2],\ [857, 857, -w^3 + 4*w^2 + 3*w - 8],\ [863, 863, -w^3 + w^2 - w - 1],\ [863, 863, w^3 - 2*w^2 + 2*w - 2],\ [911, 911, -w^3 + 3*w^2 - 11],\ [911, 911, w^3 - 3*w - 9],\ [919, 919, -2*w^3 + w^2 + 8*w - 2],\ [919, 919, -2*w^3 + 5*w^2 + 4*w - 5],\ [929, 929, -2*w^3 + 2*w^2 + 9*w - 4],\ [929, 929, 2*w^3 - 9*w - 12],\ [929, 929, 2*w^3 - 6*w^2 - 3*w + 19],\ [929, 929, -2*w^3 + 4*w^2 + 7*w - 5],\ [937, 937, -w^3 + 2*w^2 - 6],\ [937, 937, -w^3 + 3*w^2 - 10],\ [937, 937, w^3 - 3*w - 8],\ [937, 937, w^3 - w^2 - w - 5],\ [953, 953, 2*w^3 - 6*w^2 - 3*w + 18],\ [953, 953, -3*w^3 + 3*w^2 + 11*w - 5],\ [961, 31, 4*w^2 - 4*w - 11],\ [967, 967, -w^3 + 7*w - 3],\ [967, 967, -2*w^3 + 2*w^2 + 11*w + 2],\ [967, 967, -w^3 - 4*w^2 + 9*w + 9],\ [967, 967, -w^3 + 3*w^2 + 4*w - 3],\ [977, 977, 2*w^2 - 5*w - 8],\ [977, 977, -w^3 + 2*w^2 - w + 6],\ [977, 977, -w^3 + w^2 - 6],\ [977, 977, 2*w^2 + w - 11],\ [983, 983, -w^3 + 6*w^2 - 2*w - 16],\ [983, 983, w^3 + 3*w^2 - 7*w - 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -4, 0, -4, 1, 8, -4, -4, -4, 4, 12, 4, 8, -8, 0, 0, 12, 2, -8, -12, 12, -8, -16, 12, 4, -4, -12, -20, 6, -24, -8, 8, -16, -20, -16, -16, 14, 22, -12, 4, -8, 20, -20, 6, -10, -20, 16, -20, 28, -20, -18, -2, -4, 12, 24, 0, -24, -20, 8, -6, -30, -12, -20, 28, -28, -20, 14, 22, 0, 8, 28, -28, -4, 6, -2, 4, 24, -20, -4, -24, -12, -40, 38, -26, -20, -32, -28, 12, 0, 24, -36, -16, 20, 0, 16, -40, -42, -10, 8, 4, 30, -2, 4, 0, -22, 2, 36, -4, 40, 20, 8, 20, 24, 36, 34, 20, -20, 2, 30, -34, 26, 4, 36, -36, -12, 14, 22, -36, -20, -8, -8, -8, 44, -36, 4, 4, 8, -14, 26, 6, 38, -4, 28, 0, -40, 36, -48, 4, 24, 12, 24, -4, 4, 24, -56, 40, 32, 30, -58, 14, -34, -16, 10, -22, 0, -48, 24, 8, -48, 4, 28, 16, -4, 18, -54, 12, -24, -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([7,7,-w + 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]