/* 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([25, 5, -2*w^2 + 2*w + 7]) 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^2 - 5 K. = NumberField(heckePol) hecke_eigenvalues_array = [0, e, e, 2, 2, 7, -3*e, -3*e, -2*e, -2*e, 12, 5*e, 5*e, -3, -3, -2*e, -2*e, 4*e, 4*e, -3, -3, 6*e, 6*e, 2, 7, -8, -8, 7, -5*e, -5*e, 2, 2, 2*e, 2*e, -7*e, -7*e, -13, -13, -8, -8, 10*e, 10*e, -13, -13, -12*e, -12*e, -e, -e, -18, -8, -8, -18, 7, -18, -18, 7, -8, -8, -6*e, -6*e, 32, 32, -8, -8, 10*e, 0, 0, 10*e, 37, 8*e, -2*e, -2*e, 8*e, 9*e, 9*e, 9*e, 9*e, 2*e, 17*e, 17*e, 2*e, -28, -28, -e, -e, 10*e, -10*e, -10*e, 10*e, -7*e, -7*e, -10*e, -10*e, 16*e, 16*e, 27, 27, -18, 17, 17, -18, 7, 7, -28, -28, -8*e, -13*e, -13*e, -8*e, -38, -38, -4*e, -4*e, -18, 2, 2, -18, 7, 7, 32, -18, -18, 32, 6*e, 6*e, 12*e, 12*e, -21*e, 4*e, 4*e, -21*e, -43, -43, 7, 37, 37, 7, 12*e, -18*e, -18*e, 12*e, -24*e, -24*e, 18*e, 3*e, 3*e, 18*e, 4*e, 4*e, 57, 42, -18, -18, 42, 12, -48, -48, 12, 12*e, 12*e, -22*e, -22*e, 42, 17, 17, 42, -18, 57, -53, -53, 32, 32] 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 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]