/* 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([11, 7, -6, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([55, 55, -3*w^2 + 2*w + 11]) primes_array = [ [5, 5, -w^2 + 2*w + 3],\ [9, 3, w^3 - 3*w^2 - 2*w + 9],\ [9, 3, -w^3 + 5*w + 5],\ [11, 11, w],\ [11, 11, w - 1],\ [16, 2, 2],\ [19, 19, -w^3 + 2*w^2 + 3*w - 2],\ [19, 19, w^3 - w^2 - 4*w + 2],\ [29, 29, w^3 - 4*w^2 - w + 10],\ [29, 29, -w^3 + 3*w^2 + w - 7],\ [41, 41, 3*w^2 - 2*w - 10],\ [49, 7, -2*w^2 + 3*w + 8],\ [49, 7, w^3 - 2*w^2 - 2*w + 5],\ [71, 71, -w - 3],\ [71, 71, w - 4],\ [79, 79, -w^3 + w^2 + 3*w + 3],\ [79, 79, -w^3 + 2*w^2 + 2*w - 6],\ [89, 89, w^3 - 3*w^2 - 3*w + 7],\ [89, 89, w^3 - 6*w - 2],\ [101, 101, 2*w^3 - 5*w^2 - 3*w + 9],\ [101, 101, -w^3 + 3*w^2 + 3*w - 12],\ [109, 109, -w^3 + 4*w^2 + w - 9],\ [109, 109, -w^3 + 2*w^2 + 4*w - 2],\ [121, 11, -3*w^2 + 3*w + 10],\ [131, 131, -2*w^3 + 5*w^2 + 4*w - 9],\ [131, 131, -w^3 + w^2 + 3*w + 5],\ [131, 131, -w^3 + 2*w^2 + 2*w - 8],\ [131, 131, -w^3 + 6*w^2 - 18],\ [149, 149, -w^3 - 2*w^2 + 7*w + 8],\ [149, 149, -2*w^3 + 6*w^2 + 5*w - 16],\ [151, 151, w^2 + w - 5],\ [151, 151, w^2 - 3*w - 3],\ [169, 13, w^3 - 4*w^2 - w + 6],\ [169, 13, 2*w^3 - 5*w^2 - 4*w + 6],\ [179, 179, w^3 - 4*w - 6],\ [179, 179, -w^3 + 3*w^2 + w - 9],\ [181, 181, w^3 + 3*w^2 - 7*w - 15],\ [181, 181, w^3 - 6*w^2 + 2*w + 18],\ [191, 191, 5*w^2 - 7*w - 15],\ [191, 191, -4*w^2 + 5*w + 12],\ [199, 199, -w^3 + 3*w^2 + 3*w - 6],\ [199, 199, w^3 - 6*w - 1],\ [211, 211, w^3 - 7*w - 4],\ [211, 211, -w^3 + 3*w^2 + 4*w - 10],\ [229, 229, -w^3 - w^2 + 5*w + 9],\ [229, 229, -w^3 + 4*w^2 - 12],\ [239, 239, 4*w^2 - 5*w - 17],\ [239, 239, 4*w^2 - 3*w - 18],\ [241, 241, -w^3 + 3*w^2 + w - 2],\ [241, 241, -w^3 + 3*w^2 + 4*w - 9],\ [241, 241, w^3 - 7*w - 3],\ [241, 241, -w^3 + 4*w - 1],\ [271, 271, -w - 4],\ [271, 271, w^3 - 3*w^2 - 2*w + 2],\ [271, 271, -2*w^3 + 6*w^2 + 2*w - 7],\ [271, 271, w - 5],\ [281, 281, w^3 - 2*w^2 - 3*w - 1],\ [281, 281, -w^3 + w^2 + 4*w - 5],\ [289, 17, -2*w^3 + w^2 + 9*w + 1],\ [289, 17, -2*w^3 + 5*w^2 + 5*w - 9],\ [311, 311, w^3 - w^2 - 6*w + 1],\ [311, 311, -w^3 + 2*w^2 + 5*w - 5],\ [331, 331, -3*w^3 + 5*w^2 + 10*w - 5],\ [331, 331, 3*w^3 - 2*w^2 - 12*w - 6],\ [349, 349, -2*w^3 + 2*w^2 + 10*w + 3],\ [349, 349, -2*w^3 - w^2 + 12*w + 10],\ [349, 349, 2*w^3 + w^2 - 10*w - 12],\ [349, 349, -2*w^3 + 4*w^2 + 8*w - 13],\ [361, 19, -4*w^2 + 4*w + 13],\ [379, 379, w^3 + w^2 - 5*w - 10],\ [379, 379, -3*w^3 + 4*w^2 + 12*w - 7],\ [379, 379, w^3 + 4*w^2 - 8*w - 21],\ [379, 379, w^3 - 3*w - 6],\ [389, 389, 2*w^3 - 6*w^2 - 4*w + 13],\ [389, 389, -5*w^2 + 7*w + 13],\ [389, 389, 2*w^3 - 7*w^2 - 5*w + 20],\ [389, 389, 2*w^3 - 10*w - 5],\ [419, 419, -w^3 + 5*w^2 + w - 13],\ [419, 419, 4*w^2 - 7*w - 14],\ [419, 419, 2*w^3 - 3*w^2 - 5*w - 1],\ [419, 419, -w^3 - 2*w^2 + 8*w + 8],\ [421, 421, -2*w^2 + 5*w + 7],\ [421, 421, w^3 - 6*w^2 + 5*w + 13],\ [439, 439, 2*w^3 - 2*w^2 - 9*w + 3],\ [439, 439, w^3 + w^2 - 7*w - 4],\ [449, 449, 3*w^3 - 6*w^2 - 9*w + 8],\ [449, 449, 5*w^2 - 8*w - 17],\ [449, 449, 2*w^3 - w^2 - 8*w - 7],\ [449, 449, -3*w^3 + 3*w^2 + 12*w - 4],\ [479, 479, -2*w^3 + 3*w^2 + 5*w + 3],\ [479, 479, 3*w^3 - 7*w^2 - 9*w + 15],\ [499, 499, -w^3 + 4*w^2 + 4*w - 9],\ [499, 499, w^3 + w^2 - 9*w - 2],\ [509, 509, 2*w^3 + 2*w^2 - 11*w - 16],\ [509, 509, -2*w^3 + 8*w^2 + w - 23],\ [521, 521, -3*w^3 + w^2 + 13*w + 6],\ [521, 521, w^3 + 4*w^2 - 10*w - 16],\ [541, 541, 3*w^3 - 2*w^2 - 13*w - 3],\ [541, 541, -w^3 + 7*w^2 - w - 25],\ [541, 541, w^3 + 4*w^2 - 10*w - 20],\ [541, 541, -3*w^3 + 7*w^2 + 8*w - 15],\ [571, 571, w^3 + 4*w^2 - 9*w - 15],\ [571, 571, w^3 - 7*w^2 + 2*w + 19],\ [601, 601, -3*w^3 + 2*w^2 + 13*w + 5],\ [601, 601, 3*w^3 - 7*w^2 - 8*w + 17],\ [619, 619, w^3 - 3*w - 7],\ [619, 619, w^3 - 5*w^2 + 3*w + 13],\ [619, 619, 3*w^3 - 4*w^2 - 9*w - 2],\ [619, 619, -w^3 + 3*w^2 - 9],\ [641, 641, 6*w^2 - 4*w - 23],\ [641, 641, -3*w^3 + w^2 + 12*w + 5],\ [659, 659, -2*w^3 + 6*w^2 + 3*w - 17],\ [659, 659, -2*w^3 + 9*w + 10],\ [661, 661, 3*w^3 - 6*w^2 - 9*w + 14],\ [661, 661, 5*w^2 - 6*w - 18],\ [661, 661, -5*w^2 + 4*w + 19],\ [661, 661, 3*w^3 - 3*w^2 - 12*w - 2],\ [691, 691, -3*w^3 + 5*w^2 + 10*w - 6],\ [691, 691, -3*w^3 + 4*w^2 + 11*w - 6],\ [701, 701, -w^3 - 4*w^2 + 9*w + 20],\ [701, 701, -w^3 + 4*w^2 + 3*w - 19],\ [701, 701, -w^3 + 4*w^2 + 4*w - 15],\ [701, 701, w^3 - 7*w^2 + 2*w + 24],\ [709, 709, 3*w^2 - 5*w - 13],\ [709, 709, 3*w^2 - w - 15],\ [719, 719, -w^3 + 3*w^2 + 4*w - 4],\ [719, 719, -w^3 + 7*w - 2],\ [739, 739, -w^3 + 4*w^2 + 3*w - 9],\ [739, 739, -2*w^3 - w^2 + 11*w + 8],\ [739, 739, 2*w^3 - 7*w^2 - 3*w + 16],\ [739, 739, -w^3 - w^2 + 8*w + 3],\ [751, 751, 3*w^3 - 5*w^2 - 10*w + 10],\ [751, 751, 2*w^2 - 5*w - 5],\ [761, 761, 3*w^3 - 3*w^2 - 11*w + 3],\ [761, 761, w^3 - 2*w^2 - 3*w - 2],\ [761, 761, -w^3 + w^2 + 4*w - 6],\ [761, 761, -3*w^3 + 6*w^2 + 8*w - 8],\ [769, 769, -w^3 - w^2 + 7*w + 1],\ [769, 769, -2*w^3 + 6*w^2 + 6*w - 15],\ [769, 769, -2*w^3 + 5*w^2 + 5*w - 7],\ [769, 769, 2*w^3 + w^2 - 12*w - 9],\ [809, 809, -2*w^3 + 8*w^2 + 4*w - 23],\ [809, 809, -3*w^3 + 11*w^2 + 2*w - 28],\ [829, 829, -3*w^3 + 7*w^2 + 7*w - 9],\ [829, 829, w^3 + 2*w^2 - 6*w - 15],\ [829, 829, -w^3 + 5*w^2 - w - 18],\ [829, 829, -3*w^3 + 2*w^2 + 12*w - 2],\ [839, 839, 2*w^3 - 9*w^2 + 20],\ [839, 839, -3*w^3 + 10*w^2 + 5*w - 30],\ [841, 29, 5*w^2 - 5*w - 16],\ [881, 881, -w^3 - 4*w^2 + 8*w + 18],\ [881, 881, 2*w^3 - 7*w^2 - w + 9],\ [881, 881, 2*w^3 - 6*w^2 - 3*w + 6],\ [881, 881, -w^3 + 7*w^2 - 3*w - 21],\ [911, 911, -w^3 - 4*w^2 + 8*w + 16],\ [911, 911, -w^3 - w^2 + 9*w + 5],\ [911, 911, -w^3 + 4*w^2 + 4*w - 12],\ [911, 911, w^3 - 7*w^2 + 3*w + 19],\ [919, 919, -4*w^3 + 7*w^2 + 14*w - 9],\ [919, 919, 4*w^3 - 5*w^2 - 16*w + 8],\ [929, 929, 3*w^2 - w - 16],\ [929, 929, 3*w^2 - 5*w - 14],\ [941, 941, -w^3 - w^2 + 9*w + 7],\ [941, 941, -3*w^3 + 7*w^2 + 7*w - 15],\ [941, 941, 3*w^3 - 2*w^2 - 12*w - 4],\ [941, 941, w^3 + 4*w^2 - 13*w - 16],\ [961, 31, -2*w^2 + 2*w + 13],\ [961, 31, 5*w^2 - 5*w - 18],\ [971, 971, w^3 + 4*w^2 - 9*w - 19],\ [971, 971, w^3 - 7*w^2 + 2*w + 23],\ [991, 991, 3*w^3 - 7*w^2 - 7*w + 14],\ [991, 991, -3*w^3 + 2*w^2 + 12*w + 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -2, -2, -1, 0, 5, 2, -4, -6, 6, 6, -10, 8, 12, 0, -10, 8, 12, 12, 18, -18, -10, -4, -10, 12, 0, 12, 0, 0, 0, 8, 8, 8, 8, 6, 18, -22, 2, 24, 12, -22, -10, 20, -4, -4, -10, 18, 24, -10, 2, -10, 14, 8, 8, 20, 20, -6, -6, 2, 2, -24, -12, -4, -16, 32, -4, -28, 26, 26, -16, 8, 32, -34, 24, -12, 0, -12, -24, 18, 30, -18, 26, 2, -28, 20, 6, -24, 6, 12, 24, -6, -10, 2, -42, 24, 18, 42, 2, 2, 14, 14, -28, -4, -10, 26, -4, 26, -46, -10, 42, 18, 0, 48, -10, 14, -22, 14, -4, 8, -18, -6, -18, 30, 44, 8, 30, -12, -16, 50, 38, -4, 32, -16, -6, 6, -30, -6, 50, -28, -16, -4, 18, 24, 32, -34, 56, -46, 42, 42, 2, 6, -18, -18, 18, 12, -24, -36, -12, -22, -22, -42, -6, 18, -30, -42, -42, -46, 14, -12, 36, -16, -16] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5, 5, -w^2 + 2*w + 3])] = 1 AL_eigenvalues[ZF.ideal([11, 11, w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]