/* 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, 0, -7, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([31, 31, -w^3 + w^2 + 4*w - 2]) primes_array = [ [4, 2, -w^2 + w + 3],\ [5, 5, w + 1],\ [5, 5, -w^3 + w^2 + 4*w - 4],\ [11, 11, w],\ [29, 29, w^3 - 2*w^2 - 3*w + 7],\ [29, 29, -w^3 - 2*w^2 + 3*w + 7],\ [31, 31, -w^3 + w^2 + 4*w - 2],\ [31, 31, -w^3 - w^2 + 4*w + 2],\ [41, 41, w^3 + 2*w^2 - 4*w - 6],\ [41, 41, w^3 - 5*w + 2],\ [49, 7, -w^3 + w^2 + 4*w - 1],\ [49, 7, w^3 + w^2 - 4*w - 1],\ [59, 59, -3*w^2 - w + 10],\ [59, 59, -3*w^2 + w + 10],\ [61, 61, -2*w^3 + 2*w^2 + 7*w - 5],\ [61, 61, 2*w^3 + w^2 - 8*w - 6],\ [71, 71, 2*w^2 + w - 9],\ [71, 71, 2*w^2 - w - 9],\ [81, 3, -3],\ [101, 101, 2*w^2 - w - 10],\ [101, 101, 2*w^2 + w - 10],\ [109, 109, 2*w^3 + w^2 - 8*w - 3],\ [109, 109, -2*w^3 + w^2 + 8*w - 3],\ [121, 11, -w^2 + 7],\ [131, 131, 4*w^2 - 2*w - 15],\ [131, 131, 2*w^2 + 2*w - 3],\ [131, 131, 2*w^2 - 2*w - 3],\ [131, 131, -w^3 - w^2 + 3*w + 7],\ [139, 139, w^3 + 4*w^2 - 5*w - 16],\ [139, 139, w^3 + 3*w^2 - 6*w - 10],\ [139, 139, 2*w^3 - w^2 - 8*w + 1],\ [139, 139, -4*w^2 - w + 12],\ [149, 149, 2*w^3 - w^2 - 8*w + 4],\ [149, 149, 2*w^3 + w^2 - 8*w - 4],\ [151, 151, 3*w^2 - 3*w - 8],\ [151, 151, 2*w^3 - 4*w^2 - 8*w + 17],\ [151, 151, w^2 - 2*w - 7],\ [151, 151, w^3 + 2*w^2 - 6*w - 8],\ [179, 179, w^3 - w^2 - 5*w + 1],\ [179, 179, -w^3 - w^2 + 5*w + 1],\ [191, 191, 2*w^3 - w^2 - 7*w + 2],\ [191, 191, 3*w^3 - 2*w^2 - 10*w + 2],\ [199, 199, w^3 - 4*w^2 - 3*w + 13],\ [199, 199, -w^3 - 4*w^2 + 3*w + 13],\ [211, 211, -w^3 + w^2 + 6*w - 5],\ [211, 211, w^3 - 5*w - 5],\ [211, 211, -w^3 + 5*w - 5],\ [211, 211, w^3 + w^2 - 6*w - 5],\ [229, 229, w^3 - 4*w^2 - 2*w + 14],\ [229, 229, 2*w^3 + 3*w^2 - 7*w - 12],\ [229, 229, 2*w^3 - 3*w^2 - 7*w + 12],\ [229, 229, 2*w^3 + w^2 - 7*w - 8],\ [241, 241, w^3 + w^2 - 6*w - 4],\ [241, 241, -w^3 + w^2 + 6*w - 4],\ [251, 251, 2*w^2 - w - 2],\ [251, 251, 2*w^2 + w - 2],\ [271, 271, 2*w^3 - 2*w^2 - 8*w + 5],\ [271, 271, -4*w^2 - w + 14],\ [271, 271, -4*w^2 + w + 14],\ [271, 271, 2*w^3 + 2*w^2 - 8*w - 5],\ [281, 281, -2*w^3 - w^2 + 9*w + 2],\ [281, 281, 2*w^3 - w^2 - 9*w + 2],\ [311, 311, -w^3 + 3*w - 5],\ [311, 311, w^3 - 3*w - 5],\ [331, 331, -3*w^3 + 3*w^2 + 12*w - 13],\ [331, 331, 3*w^3 + 3*w^2 - 12*w - 13],\ [349, 349, 2*w^3 + 2*w^2 - 7*w - 10],\ [349, 349, -2*w^3 + 2*w^2 + 7*w - 10],\ [361, 19, 4*w^2 - 15],\ [361, 19, -4*w^2 + 13],\ [379, 379, -w^3 + 3*w^2 + 3*w - 13],\ [379, 379, w^3 + 3*w^2 - 3*w - 13],\ [409, 409, 3*w^3 - 2*w^2 - 11*w + 2],\ [409, 409, w^3 + 3*w^2 - 6*w - 9],\ [419, 419, -w^3 + w^2 + 6*w + 2],\ [419, 419, -3*w^3 + 5*w^2 + 13*w - 19],\ [421, 421, -w^3 + 3*w^2 + 7*w - 13],\ [421, 421, 2*w^3 - 2*w^2 - 9*w + 6],\ [421, 421, -2*w^3 - 2*w^2 + 9*w + 6],\ [421, 421, w^3 + 3*w^2 - 7*w - 13],\ [439, 439, 3*w^2 + 2*w - 13],\ [439, 439, 3*w^3 + 2*w^2 - 12*w - 10],\ [439, 439, -3*w^3 + 2*w^2 + 12*w - 10],\ [439, 439, 3*w^2 - 2*w - 13],\ [449, 449, 2*w^3 - 4*w^2 - 9*w + 14],\ [449, 449, -3*w^3 + 3*w^2 + 11*w - 9],\ [449, 449, 3*w^3 + 3*w^2 - 11*w - 9],\ [449, 449, w^3 - 2*w^2 - 5*w + 2],\ [461, 461, -w - 5],\ [461, 461, w - 5],\ [499, 499, w^3 - 5*w^2 - w + 17],\ [499, 499, -w^3 - 5*w^2 + w + 17],\ [509, 509, w^3 + 5*w^2 - 4*w - 16],\ [509, 509, w^2 - 2*w - 10],\ [509, 509, w^2 + 2*w - 10],\ [509, 509, w^3 - w^2 - 5*w + 9],\ [541, 541, 3*w^3 - 10*w - 6],\ [541, 541, -2*w^3 + 5*w^2 + 5*w - 16],\ [569, 569, 3*w^3 + 2*w^2 - 13*w - 6],\ [569, 569, -2*w^3 + 4*w^2 + 7*w - 10],\ [599, 599, w^3 + 2*w^2 - 7*w - 10],\ [599, 599, -w^3 + 2*w^2 + 7*w - 10],\ [601, 601, -3*w^3 - w^2 + 12*w + 6],\ [601, 601, 3*w^3 - w^2 - 12*w + 6],\ [619, 619, 3*w^3 - 12*w + 2],\ [619, 619, -3*w^3 + 12*w + 2],\ [631, 631, -w^3 + w^2 + 2*w - 8],\ [631, 631, w^3 + w^2 - 2*w - 8],\ [641, 641, w^3 + w^2 - 7*w - 1],\ [641, 641, -3*w^3 - 2*w^2 + 12*w + 4],\ [641, 641, 3*w^3 - 2*w^2 - 12*w + 4],\ [641, 641, w^3 - w^2 - 7*w + 1],\ [659, 659, -2*w^3 + w^2 + 10*w - 1],\ [659, 659, -w^3 + 5*w^2 + 4*w - 19],\ [659, 659, w^3 + 5*w^2 - 4*w - 19],\ [659, 659, 2*w^3 + w^2 - 10*w - 1],\ [691, 691, 3*w^2 - 2*w - 14],\ [691, 691, 3*w^2 + 2*w - 14],\ [701, 701, w^3 + 4*w^2 - 7*w - 12],\ [701, 701, 3*w^3 - w^2 - 12*w - 1],\ [719, 719, -w^3 + 7*w - 3],\ [719, 719, w^3 - 7*w - 3],\ [739, 739, 3*w^3 + w^2 - 12*w - 3],\ [739, 739, w^3 + 2*w^2 - 3*w - 1],\ [739, 739, -w^3 + 2*w^2 + 3*w - 1],\ [739, 739, -3*w^3 + w^2 + 12*w - 3],\ [751, 751, -2*w^3 + 6*w^2 + 7*w - 20],\ [751, 751, 2*w^3 + 6*w^2 - 7*w - 20],\ [761, 761, 2*w^3 + 6*w^2 - 8*w - 21],\ [761, 761, -2*w^3 + 6*w^2 + 8*w - 21],\ [769, 769, -2*w^3 + 6*w^2 + 8*w - 23],\ [769, 769, w^2 + 2*w + 3],\ [809, 809, 2*w^3 + 3*w^2 - 7*w - 14],\ [809, 809, -2*w^3 + 3*w^2 + 7*w - 14],\ [821, 821, -3*w^3 - w^2 + 11*w + 1],\ [821, 821, 3*w^3 - w^2 - 11*w + 1],\ [829, 829, 3*w^3 - w^2 - 12*w + 4],\ [829, 829, w^3 - 4*w^2 - 6*w + 12],\ [829, 829, -w^3 - 4*w^2 + 6*w + 12],\ [829, 829, -3*w^3 - w^2 + 12*w + 4],\ [839, 839, -w^3 + 3*w - 6],\ [839, 839, w^3 - 3*w - 6],\ [841, 29, 5*w^2 - 19],\ [859, 859, w^3 + 2*w^2 - 7*w - 9],\ [859, 859, -w^3 + 2*w^2 + 7*w - 9],\ [911, 911, -2*w^3 + 4*w^2 + 9*w - 13],\ [911, 911, 2*w^3 + 4*w^2 - 9*w - 13],\ [919, 919, 2*w^3 + 4*w^2 - 7*w - 17],\ [919, 919, 3*w^3 + 2*w^2 - 11*w - 6],\ [919, 919, 3*w^3 - 2*w^2 - 11*w + 6],\ [919, 919, 2*w^3 - 4*w^2 - 7*w + 17],\ [941, 941, -2*w^3 + 2*w^2 + 7*w - 15],\ [941, 941, 2*w^3 + 2*w^2 - 7*w - 15],\ [961, 31, -2*w^2 + 13],\ [971, 971, w^3 + 2*w^2 - 7*w - 7],\ [971, 971, -w^3 + 2*w^2 + 7*w - 7],\ [991, 991, 3*w^3 + 2*w^2 - 11*w - 7],\ [991, 991, -3*w^3 + 2*w^2 + 11*w - 7]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -3, 3, -5, 9, -4, 1, -3, -5, 0, 1, -10, -11, 4, -2, 8, -15, -7, 1, 10, 5, -10, 12, 15, 10, -11, -6, -6, 2, -8, 4, -20, -9, -4, -24, 4, -12, 7, -4, 8, 20, -20, 18, -14, -20, 4, -19, -12, -2, -28, -20, 3, 3, 19, -16, -15, -2, 26, -24, -27, -18, 16, 33, -4, -27, 30, -26, -17, -4, 10, 22, 7, 30, -20, -18, -14, 28, -29, 32, 6, -16, 12, -8, 33, 11, 14, 23, 23, -6, 39, -5, -28, 0, 5, -44, -18, -14, 23, 12, -29, 29, 12, 10, 36, -40, 20, -20, -17, 3, 32, -13, -27, 38, -5, 36, 0, -12, -22, 39, -18, -5, 8, 16, -15, 35, -22, 46, 10, -32, 20, -54, 39, -47, 54, 6, 38, 20, -16, -4, 46, 6, 8, -51, 25, -32, -39, -37, 16, -48, -42, 18, 9, -46, 19, -24, 31, 37, 10] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([31, 31, -w^3 + w^2 + 4*w - 2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]