/* 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, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([20, 10, -2*w + 10]) primes_array = [ [4, 2, 2],\ [5, 5, -w + 5],\ [5, 5, -w - 4],\ [9, 3, 3],\ [13, 13, w + 3],\ [13, 13, w - 4],\ [17, 17, w + 6],\ [17, 17, -w + 7],\ [19, 19, w + 2],\ [19, 19, w - 3],\ [23, 23, w + 1],\ [23, 23, -w + 2],\ [31, 31, -w - 7],\ [31, 31, w - 8],\ [37, 37, 2*w - 9],\ [37, 37, 2*w + 7],\ [43, 43, 4*w + 17],\ [43, 43, 4*w - 21],\ [47, 47, -w - 8],\ [47, 47, w - 9],\ [49, 7, -7],\ [71, 71, 3*w - 14],\ [71, 71, -5*w + 29],\ [79, 79, 5*w + 21],\ [79, 79, 5*w - 26],\ [97, 97, 2*w - 3],\ [97, 97, -2*w - 1],\ [101, 101, 2*w - 1],\ [107, 107, -w - 11],\ [107, 107, w - 12],\ [121, 11, -11],\ [131, 131, -w - 12],\ [131, 131, w - 13],\ [137, 137, 3*w - 11],\ [137, 137, -3*w - 8],\ [157, 157, -w - 13],\ [157, 157, w - 14],\ [179, 179, -4*w - 13],\ [179, 179, 4*w - 17],\ [181, 181, 7*w + 29],\ [181, 181, 7*w - 36],\ [193, 193, 3*w - 22],\ [193, 193, -3*w - 19],\ [197, 197, -3*w - 4],\ [197, 197, 3*w - 7],\ [211, 211, -9*w + 52],\ [211, 211, 5*w - 23],\ [223, 223, 2*w - 19],\ [223, 223, -2*w - 17],\ [227, 227, 3*w - 2],\ [227, 227, 3*w - 1],\ [233, 233, 6*w - 29],\ [233, 233, 6*w + 23],\ [239, 239, 9*w - 47],\ [239, 239, 9*w + 38],\ [251, 251, -5*w + 22],\ [251, 251, 5*w + 17],\ [281, 281, -w - 17],\ [281, 281, w - 18],\ [283, 283, -4*w - 9],\ [283, 283, 4*w - 13],\ [307, 307, 7*w - 34],\ [307, 307, 7*w + 27],\ [317, 317, -w - 18],\ [317, 317, w - 19],\ [359, 359, 5*w - 19],\ [359, 359, -5*w - 14],\ [367, 367, -11*w + 64],\ [367, 367, 7*w - 33],\ [373, 373, -3*w - 23],\ [373, 373, 3*w - 26],\ [379, 379, 4*w - 7],\ [379, 379, -4*w - 3],\ [383, 383, 2*w - 23],\ [383, 383, -2*w - 21],\ [409, 409, 10*w + 41],\ [409, 409, 10*w - 51],\ [421, 421, 5*w - 17],\ [421, 421, -5*w - 12],\ [449, 449, -5*w - 11],\ [449, 449, 5*w - 16],\ [491, 491, 5*w - 36],\ [491, 491, -5*w - 31],\ [499, 499, 5*w - 14],\ [499, 499, -5*w - 9],\ [509, 509, 6*w - 23],\ [509, 509, -6*w - 17],\ [521, 521, -5*w - 8],\ [521, 521, 5*w - 13],\ [541, 541, 5*w - 12],\ [541, 541, -5*w - 7],\ [557, 557, 4*w - 33],\ [557, 557, -4*w - 29],\ [563, 563, 9*w + 34],\ [563, 563, 9*w - 43],\ [569, 569, 15*w + 64],\ [569, 569, 15*w - 79],\ [587, 587, -7*w - 22],\ [587, 587, 7*w - 29],\ [593, 593, 14*w + 59],\ [593, 593, 14*w - 73],\ [601, 601, -5*w - 3],\ [601, 601, 5*w - 8],\ [607, 607, 13*w - 67],\ [607, 607, 13*w + 54],\ [619, 619, -5*w - 1],\ [619, 619, 5*w - 6],\ [631, 631, 5*w - 2],\ [631, 631, 5*w - 3],\ [643, 643, 3*w - 31],\ [643, 643, -3*w - 28],\ [653, 653, -6*w - 13],\ [653, 653, 6*w - 19],\ [677, 677, -w - 26],\ [677, 677, w - 27],\ [683, 683, 2*w - 29],\ [683, 683, -2*w - 27],\ [691, 691, 6*w - 43],\ [691, 691, -6*w - 37],\ [701, 701, -5*w - 34],\ [701, 701, 5*w - 39],\ [727, 727, 13*w + 53],\ [727, 727, 13*w - 66],\ [743, 743, 7*w + 41],\ [743, 743, 19*w + 82],\ [761, 761, -16*w + 93],\ [761, 761, 10*w - 47],\ [787, 787, -w - 28],\ [787, 787, w - 29],\ [809, 809, -6*w - 7],\ [809, 809, 6*w - 13],\ [821, 821, 4*w - 37],\ [821, 821, -4*w - 33],\ [827, 827, 12*w - 59],\ [827, 827, 12*w + 47],\ [829, 829, 3*w - 34],\ [829, 829, -3*w - 31],\ [839, 839, 16*w - 83],\ [839, 839, 16*w + 67],\ [841, 29, -29],\ [853, 853, 14*w + 57],\ [853, 853, 14*w - 71],\ [857, 857, 7*w - 23],\ [857, 857, -7*w - 16],\ [887, 887, 8*w - 31],\ [887, 887, -8*w - 23],\ [929, 929, -5*w - 37],\ [929, 929, 5*w - 42],\ [967, 967, -w - 31],\ [967, 967, w - 32],\ [977, 977, 17*w + 71],\ [977, 977, 17*w - 88],\ [991, 991, 8*w - 29],\ [991, 991, -8*w - 21],\ [997, 997, -7*w - 12],\ [997, 997, 7*w - 19]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -1, 0, -4, 5, -4, -1, -4, 8, 2, 4, -5, 0, -9, -2, 7, 0, 0, -3, 6, 10, 4, -8, -10, 14, 8, -13, -2, 13, -2, -21, 10, 22, 18, 12, 18, -6, 10, 16, 8, 8, -10, -1, 18, 18, 16, 16, 18, -9, -16, 5, -3, -12, -9, 0, -12, 18, 20, 8, 27, 12, -12, -30, 9, -24, 16, 22, 16, 13, 29, 2, -26, 10, 21, 6, -17, -38, 25, -35, 15, 27, 9, 15, -27, -3, -5, 31, -30, 36, 7, 1, 2, -16, 41, 26, -31, 26, 0, 33, -18, -12, 12, -36, 8, -22, -35, 31, -25, 5, 31, -14, 5, -46, -30, 15, -49, 20, 12, -36, -2, -20, -17, -26, 38, -1, 8, 20, 26, 11, 46, 28, 15, -21, -49, -22, -4, -34, 23, 29, -5, -43, -28, 14, -7, 54, -12, 48, 6, -22, 8, -17, -2, 52, -26, -39, 0] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([4, 2, 2])] = 1 AL_eigenvalues[ZF.ideal([5, 5, -w + 5])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]