/* 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([25, 5, -11, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [5, 5, 1/5*w^3 + 4/5*w^2 - 11/5*w - 7],\ [5, 5, 1/5*w^3 - 6/5*w^2 - 1/5*w + 4],\ [11, 11, w + 1],\ [11, 11, 1/5*w^3 - 1/5*w^2 - 11/5*w + 2],\ [16, 2, 2],\ [19, 19, -1/5*w^3 + 1/5*w^2 + 1/5*w + 1],\ [19, 19, 1/5*w^3 - 1/5*w^2 - 11/5*w],\ [19, 19, -2/5*w^3 + 2/5*w^2 + 17/5*w],\ [19, 19, w - 1],\ [29, 29, w^2 - w - 8],\ [29, 29, 2/5*w^3 - 2/5*w^2 - 7/5*w + 2],\ [31, 31, 1/5*w^3 - 1/5*w^2 - 1/5*w + 2],\ [31, 31, 2/5*w^3 - 2/5*w^2 - 17/5*w + 3],\ [61, 61, -2/5*w^3 - 3/5*w^2 + 12/5*w + 5],\ [61, 61, -4/5*w^3 - 6/5*w^2 + 39/5*w + 15],\ [61, 61, 3/5*w^3 + 2/5*w^2 - 18/5*w - 3],\ [61, 61, 7/5*w^3 + 3/5*w^2 - 62/5*w - 13],\ [71, 71, 1/5*w^3 - 6/5*w^2 - 6/5*w + 4],\ [71, 71, w^2 - 8],\ [79, 79, 3/5*w^3 + 12/5*w^2 - 33/5*w - 22],\ [79, 79, 1/5*w^3 + 4/5*w^2 - 11/5*w - 9],\ [81, 3, -3],\ [101, 101, 3/5*w^3 + 7/5*w^2 - 28/5*w - 15],\ [101, 101, 1/5*w^3 + 9/5*w^2 - 16/5*w - 16],\ [121, 11, 3/5*w^3 - 3/5*w^2 - 18/5*w + 1],\ [131, 131, 1/5*w^3 + 4/5*w^2 - 16/5*w - 8],\ [131, 131, w^2 - 2*w - 2],\ [149, 149, 4/5*w^3 + 1/5*w^2 - 29/5*w - 5],\ [149, 149, 4/5*w^3 - 9/5*w^2 - 19/5*w + 6],\ [151, 151, 2/5*w^3 + 3/5*w^2 - 17/5*w - 3],\ [151, 151, -2/5*w^3 + 7/5*w^2 + 7/5*w - 8],\ [151, 151, 4/5*w^3 + 1/5*w^2 - 29/5*w - 2],\ [151, 151, -4/5*w^3 + 9/5*w^2 + 19/5*w - 9],\ [179, 179, -3/5*w^3 + 8/5*w^2 + 18/5*w - 6],\ [179, 179, 2/5*w^3 + 3/5*w^2 - 12/5*w - 6],\ [211, 211, 1/5*w^3 + 4/5*w^2 - 6/5*w - 10],\ [211, 211, 2/5*w^3 - 7/5*w^2 - 12/5*w + 2],\ [229, 229, 6/5*w^3 - 11/5*w^2 - 41/5*w + 11],\ [229, 229, 2*w^2 - 2*w - 9],\ [229, 229, -4/5*w^3 - 1/5*w^2 + 19/5*w + 2],\ [229, 229, -3/5*w^3 + 3/5*w^2 + 28/5*w - 3],\ [239, 239, 11/5*w^3 + 4/5*w^2 - 96/5*w - 19],\ [239, 239, -6/5*w^3 + 1/5*w^2 + 51/5*w + 3],\ [241, 241, 1/5*w^3 + 4/5*w^2 - 1/5*w - 6],\ [241, 241, 4/5*w^3 - 4/5*w^2 - 29/5*w - 1],\ [251, 251, -1/5*w^3 + 6/5*w^2 + 11/5*w - 12],\ [251, 251, -1/5*w^3 + 11/5*w^2 + 1/5*w - 15],\ [269, 269, 2/5*w^3 + 3/5*w^2 - 17/5*w - 2],\ [269, 269, -2/5*w^3 + 7/5*w^2 + 7/5*w - 9],\ [271, 271, 1/5*w^3 - 1/5*w^2 + 4/5*w],\ [271, 271, 3/5*w^3 - 3/5*w^2 - 28/5*w + 2],\ [281, 281, w^3 - 3*w^2 - 4*w + 13],\ [281, 281, -3/5*w^3 + 3/5*w^2 + 28/5*w - 6],\ [281, 281, -6/5*w^3 + 26/5*w^2 + 11/5*w - 16],\ [281, 281, w^3 + w^2 - 8*w - 9],\ [289, 17, 2/5*w^3 + 3/5*w^2 - 7/5*w - 5],\ [289, 17, 4/5*w^3 - 9/5*w^2 - 29/5*w + 8],\ [311, 311, -w^2 + 2*w + 11],\ [311, 311, -1/5*w^3 + 6/5*w^2 + 1/5*w - 1],\ [311, 311, 1/5*w^3 + 4/5*w^2 - 16/5*w + 1],\ [311, 311, -1/5*w^3 - 4/5*w^2 + 11/5*w + 10],\ [349, 349, -1/5*w^3 - 9/5*w^2 + 11/5*w + 16],\ [349, 349, 2/5*w^3 - 12/5*w^2 - 7/5*w + 7],\ [359, 359, -4/5*w^3 + 4/5*w^2 + 19/5*w - 1],\ [359, 359, -w^3 + 3*w^2 + 5*w - 12],\ [359, 359, w^3 - w^2 - 7*w + 2],\ [359, 359, 4/5*w^3 + 6/5*w^2 - 29/5*w - 11],\ [379, 379, 4/5*w^3 + 6/5*w^2 - 34/5*w - 9],\ [379, 379, 3/5*w^3 - 3/5*w^2 - 28/5*w + 7],\ [389, 389, w^2 - 3*w - 8],\ [389, 389, -4/5*w^3 + 14/5*w^2 + 19/5*w - 16],\ [401, 401, -3*w^2 + 2*w + 23],\ [401, 401, 1/5*w^3 - 16/5*w^2 + 4/5*w + 11],\ [409, 409, -w^3 + 2*w^2 + 3*w - 7],\ [409, 409, 7/5*w^3 - 2/5*w^2 - 57/5*w - 2],\ [419, 419, -1/5*w^3 + 1/5*w^2 + 16/5*w - 2],\ [419, 419, 1/5*w^3 - 1/5*w^2 - 16/5*w],\ [421, 421, 2/5*w^3 + 3/5*w^2 - 27/5*w - 3],\ [421, 421, 1/5*w^3 + 4/5*w^2 + 4/5*w - 3],\ [439, 439, -w^3 + 3*w^2 + 5*w - 16],\ [439, 439, -4/5*w^3 - 6/5*w^2 + 29/5*w + 7],\ [439, 439, -3/5*w^3 + 13/5*w^2 + 3/5*w - 11],\ [439, 439, 4/5*w^3 + 6/5*w^2 - 39/5*w - 10],\ [449, 449, 2/5*w^3 - 12/5*w^2 - 2/5*w + 5],\ [449, 449, 4/5*w^3 - 24/5*w^2 - 4/5*w + 15],\ [461, 461, -1/5*w^3 - 4/5*w^2 - 4/5*w + 4],\ [461, 461, 2*w^2 - 2*w - 11],\ [461, 461, 3/5*w^3 + 2/5*w^2 - 33/5*w - 4],\ [479, 479, -w^3 + 3*w^2 + 6*w - 14],\ [479, 479, -3/5*w^3 + 3/5*w^2 + 28/5*w + 3],\ [499, 499, 2/5*w^3 + 8/5*w^2 - 17/5*w - 6],\ [499, 499, -3/5*w^3 + 13/5*w^2 + 13/5*w - 17],\ [509, 509, -w^3 + 2*w^2 + 4*w - 6],\ [509, 509, 6/5*w^3 - 1/5*w^2 - 46/5*w - 4],\ [521, 521, -2/5*w^3 + 2/5*w^2 + 7/5*w - 7],\ [521, 521, -3/5*w^3 + 3/5*w^2 + 23/5*w - 8],\ [529, 23, -7/5*w^3 + 17/5*w^2 + 42/5*w - 15],\ [529, 23, 2/5*w^3 + 13/5*w^2 - 27/5*w - 21],\ [541, 541, 1/5*w^3 - 11/5*w^2 - 1/5*w + 10],\ [541, 541, 3/5*w^3 - 8/5*w^2 - 13/5*w + 13],\ [541, 541, -2*w^2 + w + 13],\ [541, 541, 3/5*w^3 + 2/5*w^2 - 23/5*w + 2],\ [569, 569, w^3 - 2*w^2 - 5*w + 7],\ [569, 569, -1/5*w^3 + 1/5*w^2 + 1/5*w - 6],\ [571, 571, w^2 + w - 9],\ [571, 571, -2/5*w^3 + 12/5*w^2 + 7/5*w - 12],\ [571, 571, 1/5*w^3 + 9/5*w^2 - 11/5*w - 11],\ [571, 571, -2/5*w^3 + 7/5*w^2 + 17/5*w - 4],\ [601, 601, -3/5*w^3 + 13/5*w^2 + 18/5*w - 11],\ [601, 601, -4/5*w^3 + 4/5*w^2 + 34/5*w + 1],\ [631, 631, 2/5*w^3 + 18/5*w^2 - 27/5*w - 30],\ [631, 631, 3/5*w^3 - 23/5*w^2 - 3/5*w + 15],\ [661, 661, -2*w^3 + 17*w + 12],\ [661, 661, -9/5*w^3 + 4/5*w^2 + 74/5*w + 1],\ [691, 691, -7/5*w^3 - 18/5*w^2 + 72/5*w + 35],\ [691, 691, 6/5*w^3 - 31/5*w^2 - 6/5*w + 19],\ [701, 701, -1/5*w^3 + 6/5*w^2 + 16/5*w - 6],\ [701, 701, 2/5*w^3 - 7/5*w^2 - 22/5*w + 8],\ [709, 709, -3/5*w^3 + 13/5*w^2 + 13/5*w - 18],\ [709, 709, 1/5*w^3 + 14/5*w^2 - 11/5*w - 20],\ [709, 709, -2/5*w^3 - 8/5*w^2 + 17/5*w + 5],\ [709, 709, 1/5*w^3 + 4/5*w^2 - 21/5*w - 10],\ [719, 719, -3/5*w^3 + 8/5*w^2 + 13/5*w - 12],\ [719, 719, 3/5*w^3 + 2/5*w^2 - 23/5*w + 1],\ [719, 719, -7/5*w^3 + 17/5*w^2 + 32/5*w - 14],\ [719, 719, 7/5*w^3 + 3/5*w^2 - 52/5*w - 8],\ [739, 739, 1/5*w^3 - 1/5*w^2 - 11/5*w - 5],\ [739, 739, w - 6],\ [761, 761, -4/5*w^3 + 9/5*w^2 + 19/5*w - 11],\ [761, 761, 4/5*w^3 + 1/5*w^2 - 29/5*w],\ [769, 769, 3/5*w^3 - 13/5*w^2 - 13/5*w + 8],\ [769, 769, -2/5*w^3 - 8/5*w^2 + 17/5*w + 15],\ [769, 769, 7/5*w^3 - 17/5*w^2 - 37/5*w + 18],\ [769, 769, -6/5*w^3 - 4/5*w^2 + 41/5*w + 5],\ [809, 809, -1/5*w^3 + 6/5*w^2 - 4/5*w - 14],\ [809, 809, -2/5*w^3 - 3/5*w^2 + 22/5*w - 4],\ [809, 809, -6/5*w^3 + 6/5*w^2 + 41/5*w - 5],\ [809, 809, w^3 - w^2 - 5*w + 4],\ [821, 821, -3/5*w^3 - 17/5*w^2 + 33/5*w + 30],\ [821, 821, -4/5*w^3 + 24/5*w^2 + 9/5*w - 15],\ [829, 829, 7/5*w^3 - 12/5*w^2 - 52/5*w + 10],\ [829, 829, -1/5*w^3 + 11/5*w^2 - 4/5*w - 19],\ [829, 829, -13/5*w^3 + 3/5*w^2 + 108/5*w + 10],\ [829, 829, -w^3 + 4*w^2 + 5*w - 23],\ [839, 839, 4/5*w^3 - 9/5*w^2 - 24/5*w + 4],\ [839, 839, 3/5*w^3 + 2/5*w^2 - 18/5*w - 8],\ [841, 29, -w^3 + w^2 + 6*w - 4],\ [859, 859, 6/5*w^3 - 11/5*w^2 - 36/5*w + 9],\ [859, 859, w^3 - 6*w - 3],\ [881, 881, 4/5*w^3 - 4/5*w^2 - 9/5*w - 1],\ [881, 881, 9/5*w^3 - 24/5*w^2 - 19/5*w + 14],\ [881, 881, -w^3 + 6*w + 2],\ [881, 881, 1/5*w^3 - 1/5*w^2 - 1/5*w - 6],\ [911, 911, w^3 - w^2 - 5*w + 1],\ [911, 911, 6/5*w^3 - 6/5*w^2 - 41/5*w + 2],\ [919, 919, -7/5*w^3 + 12/5*w^2 + 42/5*w - 7],\ [919, 919, -6/5*w^3 + 1/5*w^2 + 36/5*w + 5],\ [929, 929, -2/5*w^3 - 8/5*w^2 + 17/5*w + 16],\ [929, 929, -3/5*w^3 + 13/5*w^2 + 13/5*w - 7],\ [961, 31, w^3 - w^2 - 6*w + 2],\ [971, 971, 8/5*w^3 - 13/5*w^2 - 48/5*w + 6],\ [971, 971, -2/5*w^3 - 3/5*w^2 + 22/5*w],\ [971, 971, 7/5*w^3 - 7/5*w^2 - 57/5*w + 7],\ [971, 971, -1/5*w^3 + 6/5*w^2 - 4/5*w - 10],\ [991, 991, 2/5*w^3 + 8/5*w^2 - 22/5*w - 7],\ [991, 991, -2/5*w^3 + 12/5*w^2 + 2/5*w - 15]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-3, 3, -3, -3, 1, 8, -4, -4, 2, 0, 6, 8, -10, -13, -7, -7, -13, 0, -6, 8, -16, -5, 0, 0, -1, 3, -9, -15, 15, 11, 17, -10, 14, 0, 6, 2, -4, 8, 2, -10, 2, 15, -15, 2, 8, 12, -24, 21, 15, -7, 11, 0, -18, 0, 24, -25, -25, -27, -12, -9, -30, 14, -10, -3, 0, -33, 6, 11, -25, -30, 30, 15, 3, 14, -4, -30, 0, -19, -13, -13, 5, 26, -10, -6, -6, -36, -18, 12, 27, -27, -4, 14, 6, -6, 3, 39, 20, -34, -16, -10, -22, -4, 42, -6, 32, 32, -4, 32, 8, -10, -28, 50, 14, -22, -34, -34, -6, -30, 20, 26, 14, 26, 30, -30, 9, 27, -37, -1, 39, -45, -37, 11, -13, -13, 3, 51, -30, -6, -15, -21, -34, 29, -37, -34, -18, 0, 26, 26, 50, 18, 42, -12, 18, 0, -24, -43, -25, 18, -36, -10, -15, 36, 21, 6, 2, 20] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([16, 2, 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]