/* 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([1, -2, -6, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([17, 17, -w^3 + w^2 + 5*w]) primes_array = [ [5, 5, -w^3 + 2*w^2 + 3*w],\ [7, 7, w - 1],\ [11, 11, -w^3 + 2*w^2 + 4*w],\ [13, 13, -2*w^3 + 3*w^2 + 10*w - 2],\ [16, 2, 2],\ [17, 17, -w^3 + 2*w^2 + 5*w - 3],\ [17, 17, -w^3 + w^2 + 5*w],\ [17, 17, -w^2 + 2*w + 1],\ [19, 19, w^2 - w - 2],\ [29, 29, w^3 - 2*w^2 - 5*w],\ [29, 29, w^2 - w - 3],\ [31, 31, -w^3 + 2*w^2 + 3*w - 2],\ [43, 43, 2*w^3 - 3*w^2 - 11*w],\ [47, 47, w^3 - 7*w - 4],\ [53, 53, -2*w^3 + 3*w^2 + 9*w - 1],\ [61, 61, -w - 3],\ [73, 73, -w^3 + 2*w^2 + 3*w - 3],\ [73, 73, w^3 - w^2 - 7*w - 1],\ [81, 3, -3],\ [83, 83, -2*w^3 + 3*w^2 + 9*w + 1],\ [83, 83, -w^3 + 3*w^2 + 2*w - 3],\ [89, 89, w - 4],\ [103, 103, w^3 - 2*w^2 - 6*w + 3],\ [113, 113, 2*w^3 - w^2 - 14*w - 6],\ [121, 11, -w^2 + 2*w + 7],\ [125, 5, -3*w^3 + 4*w^2 + 15*w + 1],\ [139, 139, w^3 - 2*w^2 - 5*w - 3],\ [139, 139, w^3 - 5*w - 5],\ [151, 151, w^3 - 9*w - 7],\ [157, 157, -3*w^3 + 6*w^2 + 13*w - 6],\ [163, 163, w^3 - 3*w^2 - 2*w + 9],\ [167, 167, -w^3 + 7*w + 3],\ [167, 167, -3*w^3 + 4*w^2 + 15*w - 1],\ [173, 173, 2*w^3 - 3*w^2 - 7*w - 2],\ [181, 181, -w^3 + 3*w^2 + 4*w - 5],\ [191, 191, w^3 - w^2 - 4*w - 4],\ [193, 193, -w^3 + w^2 + 7*w + 6],\ [193, 193, 2*w^3 - 2*w^2 - 13*w - 5],\ [199, 199, -2*w^3 + 5*w^2 + 5*w - 5],\ [211, 211, w^3 - w^2 - 8*w - 3],\ [211, 211, -2*w^2 + 3*w + 8],\ [227, 227, -w^3 + 3*w^2 + 4*w - 4],\ [227, 227, w^2 - 3*w - 6],\ [229, 229, w^2 - 5],\ [229, 229, 3*w^3 - 4*w^2 - 17*w - 2],\ [233, 233, 3*w^3 - 6*w^2 - 13*w + 3],\ [233, 233, 3*w^3 - 4*w^2 - 16*w + 1],\ [241, 241, -2*w^3 + 4*w^2 + 8*w + 1],\ [251, 251, 2*w^3 - 2*w^2 - 9*w - 3],\ [277, 277, 3*w^3 - 4*w^2 - 17*w - 1],\ [281, 281, -2*w^2 + 5*w + 1],\ [283, 283, -4*w^3 + 6*w^2 + 19*w - 2],\ [293, 293, -3*w^3 + 6*w^2 + 12*w - 2],\ [307, 307, w^3 - w^2 - 4*w - 5],\ [307, 307, w^3 - w^2 - 8*w - 2],\ [311, 311, 2*w^2 - 3*w - 7],\ [313, 313, -2*w^3 + w^2 + 15*w + 3],\ [317, 317, -w^3 + 3*w^2 + w - 5],\ [331, 331, 2*w^3 - 3*w^2 - 12*w],\ [337, 337, w^3 - w^2 - 8*w - 1],\ [343, 7, -w^3 + 6*w + 8],\ [347, 347, 2*w^3 - 4*w^2 - 7*w + 5],\ [349, 349, 2*w^3 - 4*w^2 - 9*w],\ [353, 353, -3*w^3 + 4*w^2 + 16*w + 5],\ [353, 353, -3*w^3 + 4*w^2 + 14*w],\ [353, 353, -w^3 + 3*w^2 + 4*w - 8],\ [353, 353, -w^3 + 2*w^2 + 8*w - 3],\ [359, 359, -4*w^3 + 7*w^2 + 19*w - 3],\ [367, 367, -w^3 + 2*w^2 + 6*w - 5],\ [373, 373, 5*w^3 - 8*w^2 - 26*w + 3],\ [379, 379, -3*w^3 + 5*w^2 + 17*w - 4],\ [379, 379, -w^3 + 2*w^2 + 4*w - 6],\ [383, 383, w^2 - 6],\ [389, 389, w^3 - 2*w^2 - 3*w - 4],\ [389, 389, w^2 + w - 4],\ [397, 397, -4*w^3 + 5*w^2 + 23*w + 5],\ [397, 397, -3*w^3 + 5*w^2 + 12*w - 2],\ [419, 419, -3*w^3 + 4*w^2 + 17*w + 5],\ [419, 419, -3*w^3 + 5*w^2 + 15*w],\ [419, 419, 3*w^3 - 5*w^2 - 14*w - 1],\ [419, 419, 2*w^3 - 3*w^2 - 10*w - 6],\ [431, 431, 2*w^3 - 2*w^2 - 11*w],\ [433, 433, w^3 - 8*w - 1],\ [433, 433, 2*w^2 - 2*w - 5],\ [439, 439, 2*w^3 - 2*w^2 - 9*w - 6],\ [443, 443, 2*w^3 - 5*w^2 - 7*w],\ [443, 443, 2*w^3 - 5*w^2 - 9*w + 4],\ [457, 457, -2*w^3 + 5*w^2 + 7*w - 4],\ [457, 457, -w^3 + 2*w^2 - 3],\ [461, 461, -4*w^3 + 7*w^2 + 17*w - 7],\ [479, 479, 3*w^3 - 5*w^2 - 12*w + 6],\ [487, 487, -2*w^3 + 5*w^2 + 9*w - 9],\ [487, 487, w^3 - 10*w - 8],\ [499, 499, 2*w^3 - 2*w^2 - 12*w + 1],\ [503, 503, w^2 - 7],\ [503, 503, w^3 + w^2 - 7*w - 8],\ [529, 23, -3*w^3 + 5*w^2 + 12*w + 1],\ [529, 23, 3*w^3 - 4*w^2 - 14*w - 1],\ [541, 541, w^3 - 4*w^2 - 2*w + 11],\ [563, 563, -2*w^3 + w^2 + 15*w + 6],\ [569, 569, w^3 - 2*w^2 - 4*w - 4],\ [601, 601, 3*w^3 - 5*w^2 - 17*w + 1],\ [607, 607, -2*w^3 + 5*w^2 + 7*w - 5],\ [607, 607, -w^3 + 3*w^2 + 6*w - 5],\ [613, 613, -4*w^3 + 5*w^2 + 21*w + 1],\ [613, 613, -5*w^3 + 8*w^2 + 23*w - 4],\ [619, 619, w^3 + w^2 - 9*w - 5],\ [619, 619, -3*w^3 + 4*w^2 + 14*w + 2],\ [641, 641, -6*w^3 + 8*w^2 + 31*w + 3],\ [643, 643, 3*w^3 - 4*w^2 - 17*w - 6],\ [643, 643, -2*w^3 + 5*w^2 + 7*w - 6],\ [647, 647, 3*w^3 - 4*w^2 - 13*w - 10],\ [653, 653, -3*w^3 + 5*w^2 + 14*w + 2],\ [653, 653, w^3 - 2*w^2 - w - 3],\ [661, 661, 5*w^3 - 9*w^2 - 24*w + 5],\ [683, 683, 2*w^3 - 3*w^2 - 13*w - 2],\ [683, 683, 4*w^3 - 7*w^2 - 18*w + 1],\ [719, 719, -w^3 + 2*w^2 + 3*w - 7],\ [719, 719, 3*w^3 - 5*w^2 - 16*w - 1],\ [727, 727, -2*w^3 + 5*w^2 + 8*w - 7],\ [727, 727, 2*w^3 - 5*w^2 - 7*w + 13],\ [733, 733, -2*w^2 + 7],\ [733, 733, -3*w^3 + 5*w^2 + 11*w + 2],\ [739, 739, -6*w^3 + 9*w^2 + 29*w - 3],\ [739, 739, -2*w^3 + 3*w^2 + 7*w + 5],\ [751, 751, 4*w^3 - 5*w^2 - 23*w - 3],\ [757, 757, -w^3 + 10*w + 4],\ [757, 757, 2*w^3 - w^2 - 14*w - 4],\ [769, 769, -w^3 + 4*w^2 + 4*w - 8],\ [769, 769, 4*w^3 - 6*w^2 - 21*w - 2],\ [787, 787, 3*w^3 - 3*w^2 - 19*w - 6],\ [787, 787, -2*w^2 + 6*w + 7],\ [839, 839, -3*w^3 + 3*w^2 + 19*w + 5],\ [841, 29, 3*w^3 - 4*w^2 - 13*w - 4],\ [853, 853, -3*w^3 + 5*w^2 + 14*w + 3],\ [853, 853, 2*w^2 - w - 9],\ [853, 853, 3*w^3 - 5*w^2 - 11*w + 1],\ [853, 853, w - 6],\ [857, 857, 2*w^3 - 2*w^2 - 9*w - 7],\ [857, 857, -4*w^3 + 8*w^2 + 13*w - 1],\ [859, 859, 2*w^3 - 4*w^2 - 13*w + 2],\ [859, 859, w^3 - w^2 - 9*w - 2],\ [863, 863, -2*w^3 - w^2 + 17*w + 11],\ [877, 877, 5*w^3 - 6*w^2 - 28*w - 9],\ [877, 877, -4*w^3 + 5*w^2 + 20*w + 6],\ [881, 881, 4*w^3 - 5*w^2 - 18*w - 8],\ [911, 911, -w^3 + 4*w^2 - w - 8],\ [911, 911, 2*w^3 - 3*w^2 - 13*w - 1],\ [919, 919, w^3 - w^2 - 7*w + 5],\ [929, 929, 2*w^3 - 3*w^2 - 13*w + 1],\ [929, 929, -2*w^3 + 5*w^2 + 6*w - 11],\ [941, 941, -3*w^3 + 7*w^2 + 12*w - 5],\ [953, 953, -2*w^3 + 5*w^2 + 5*w - 7],\ [971, 971, w^3 - w^2 - 3*w - 5],\ [971, 971, 3*w^3 - 7*w^2 - 12*w + 11],\ [977, 977, 3*w^3 - 5*w^2 - 11*w],\ [997, 997, -2*w^3 + 3*w^2 + 6*w - 5],\ [997, 997, -4*w^3 + 7*w^2 + 16*w - 2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^2 + 2*x - 11 K. = NumberField(heckePol) hecke_eigenvalues_array = [0, e, 3/2*e + 3/2, -1/2*e + 3/2, e, 0, -1, 0, e + 6, -9, 0, -4, -1/2*e - 9/2, 3/2*e + 3/2, 3, e + 9, -1/2*e + 3/2, -3/2*e + 1/2, 4, -3*e - 3, -3*e - 3, 12, -2*e, -3, -2*e - 6, 3*e - 3, e + 6, e + 15, e + 9, -2*e, -3/2*e - 35/2, 3/2*e - 21/2, -3*e + 6, 6*e + 3, -7/2*e - 3/2, 6*e + 6, -2*e - 12, -5*e - 9, -2*e + 12, -2*e, -2*e - 6, 3*e + 21, -3/2*e + 21/2, -3*e + 11, 4*e + 15, -12, 18, 3*e + 11, 3/2*e + 27/2, -5*e - 3, 3/2*e + 15/2, 4*e + 6, 3*e + 3, 7*e + 15, 11/2*e + 3/2, 3*e + 9, -2*e - 6, -15/2*e - 27/2, -5*e - 21, 4*e + 15, 11/2*e + 27/2, 3*e - 9, 8, -6*e - 9, -3/2*e + 33/2, -6*e - 18, 12, 3*e + 3, 5/2*e + 21/2, -9/2*e + 19/2, e + 9, 7*e + 18, -3*e + 6, -3, -6*e + 9, -2*e - 24, -5*e - 9, 6, -3*e + 3, 3*e + 30, -3*e + 12, -3*e + 12, 20, -8*e, -9*e - 10, -6*e + 6, -3*e + 6, -3*e + 5, -9/2*e - 29/2, -6*e - 18, 3*e + 9, 7*e + 21, -5*e + 15, -2*e - 24, -6*e - 12, 15/2*e + 15/2, -2*e - 12, 5/2*e + 9/2, 17/2*e + 21/2, 9*e + 12, 6*e, -1/2*e + 3/2, 9*e + 23, e + 15, -16, -6*e - 22, 7*e - 9, -2*e - 42, -6*e - 6, -5*e + 15, 6*e - 16, 3/2*e - 45/2, 3*e + 3, -3*e - 9, e - 15, -3*e - 27, -3*e - 33, -3*e - 39, -36, 23/2*e + 15/2, e - 9, 4*e - 12, e + 15, 2, -5*e - 33, -2*e - 30, -2*e - 36, -5*e - 3, 10*e + 12, -6*e - 37, -22, -4, -15*e - 15, 4*e - 3, 4*e + 6, -3*e - 31, -8*e, -2*e + 36, -3*e + 9, -3*e + 27, 7*e - 9, -6*e + 8, -12*e, -9/2*e + 19/2, -6*e + 17, 21/2*e + 9/2, 3*e - 15, -3*e + 18, 2, 51, 3*e - 27, -15/2*e - 51/2, 3*e - 39, 3*e, 3*e + 15, -3/2*e - 39/2, e - 21, -1/2*e - 69/2] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([17, 17, -w^3 + w^2 + 5*w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]