/* 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([-42, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([32, 8, 4*w]) primes_array = [ [2, 2, w],\ [3, 3, w],\ [7, 7, w - 7],\ [11, 11, w + 3],\ [11, 11, w + 8],\ [13, 13, w + 4],\ [13, 13, w + 9],\ [17, 17, -w - 5],\ [17, 17, -w + 5],\ [19, 19, w + 2],\ [19, 19, w + 17],\ [25, 5, 5],\ [29, 29, w + 10],\ [29, 29, w + 19],\ [41, 41, -w - 1],\ [41, 41, w - 1],\ [47, 47, -2*w + 11],\ [47, 47, 4*w - 25],\ [53, 53, w + 25],\ [53, 53, w + 28],\ [61, 61, w + 15],\ [61, 61, w + 46],\ [79, 79, -w - 11],\ [79, 79, w - 11],\ [89, 89, 3*w - 17],\ [89, 89, 5*w - 31],\ [107, 107, w + 16],\ [107, 107, w + 91],\ [127, 127, -w - 13],\ [127, 127, w - 13],\ [139, 139, w + 43],\ [139, 139, w + 96],\ [149, 149, w + 41],\ [149, 149, w + 108],\ [151, 151, 3*w + 23],\ [151, 151, -3*w + 23],\ [157, 157, w + 55],\ [157, 157, w + 102],\ [167, 167, 2*w - 1],\ [167, 167, -2*w - 1],\ [179, 179, w + 20],\ [179, 179, w + 159],\ [181, 181, w + 59],\ [181, 181, w + 122],\ [193, 193, 2*w - 19],\ [193, 193, -2*w - 19],\ [197, 197, w + 47],\ [197, 197, w + 150],\ [229, 229, w + 27],\ [229, 229, w + 202],\ [257, 257, 3*w - 11],\ [257, 257, -3*w - 11],\ [283, 283, w + 61],\ [283, 283, w + 222],\ [307, 307, w + 137],\ [307, 307, w + 170],\ [311, 311, 4*w - 19],\ [311, 311, -4*w - 19],\ [317, 317, w + 26],\ [317, 317, w + 291],\ [337, 337, -6*w + 43],\ [337, 337, -8*w + 55],\ [347, 347, w + 70],\ [347, 347, w + 277],\ [349, 349, w + 33],\ [349, 349, w + 316],\ [353, 353, 3*w - 5],\ [353, 353, -3*w - 5],\ [383, 383, -4*w - 17],\ [383, 383, 4*w - 17],\ [389, 389, w + 141],\ [389, 389, w + 248],\ [397, 397, w + 162],\ [397, 397, w + 235],\ [443, 443, w + 186],\ [443, 443, w + 257],\ [457, 457, 2*w - 25],\ [457, 457, -2*w - 25],\ [463, 463, -3*w - 29],\ [463, 463, 3*w - 29],\ [479, 479, 8*w - 47],\ [479, 479, 10*w - 61],\ [487, 487, -w - 23],\ [487, 487, w - 23],\ [491, 491, w + 32],\ [491, 491, w + 459],\ [503, 503, -4*w - 13],\ [503, 503, 4*w - 13],\ [521, 521, -5*w - 23],\ [521, 521, 5*w - 23],\ [523, 523, w + 105],\ [523, 523, w + 418],\ [529, 23, -23],\ [557, 557, w + 34],\ [557, 557, w + 523],\ [593, 593, 9*w - 53],\ [593, 593, 11*w - 67],\ [619, 619, w + 287],\ [619, 619, w + 332],\ [631, 631, 5*w - 41],\ [631, 631, -5*w - 41],\ [643, 643, w + 148],\ [643, 643, w + 495],\ [647, 647, -4*w - 5],\ [647, 647, 4*w - 5],\ [653, 653, w + 85],\ [653, 653, w + 568],\ [659, 659, w + 187],\ [659, 659, w + 472],\ [661, 661, w + 45],\ [661, 661, w + 616],\ [673, 673, 2*w - 29],\ [673, 673, -2*w - 29],\ [683, 683, w + 98],\ [683, 683, w + 585],\ [691, 691, w + 95],\ [691, 691, w + 596],\ [701, 701, w + 38],\ [701, 701, w + 663],\ [719, 719, 10*w - 59],\ [719, 719, 12*w - 73],\ [733, 733, w + 158],\ [733, 733, w + 575],\ [751, 751, 7*w - 53],\ [751, 751, -7*w - 53],\ [761, 761, 5*w - 17],\ [761, 761, -5*w - 17],\ [787, 787, w + 228],\ [787, 787, w + 559],\ [811, 811, w + 380],\ [811, 811, w + 431],\ [821, 821, w + 306],\ [821, 821, w + 515],\ [823, 823, -13*w + 89],\ [823, 823, -9*w + 65],\ [827, 827, w + 155],\ [827, 827, w + 672],\ [829, 829, w + 234],\ [829, 829, w + 595],\ [839, 839, -8*w - 43],\ [839, 839, 8*w - 43],\ [853, 853, w + 51],\ [853, 853, w + 802],\ [857, 857, 11*w - 65],\ [857, 857, 13*w - 79],\ [859, 859, w + 229],\ [859, 859, w + 630],\ [881, 881, -5*w - 13],\ [881, 881, 5*w - 13],\ [887, 887, -6*w - 25],\ [887, 887, 6*w - 25],\ [919, 919, -w - 31],\ [919, 919, w - 31],\ [929, 929, -5*w - 11],\ [929, 929, 5*w - 11],\ [947, 947, w + 44],\ [947, 947, w + 903],\ [961, 31, -31],\ [967, 967, -7*w - 55],\ [967, 967, 7*w - 55],\ [983, 983, 6*w - 23],\ [983, 983, -6*w - 23],\ [991, 991, 3*w - 37],\ [991, 991, -3*w - 37],\ [997, 997, w + 286],\ [997, 997, w + 711]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 0, 0, 0, 0, -6, -6, -2, -2, 0, 0, -6, -10, -10, -10, -10, 0, 0, 14, 14, 10, 10, 0, 0, -10, -10, 0, 0, 0, 0, 0, 0, 14, 14, 0, 0, -22, -22, 0, 0, 0, 0, 18, 18, -14, -14, -2, -2, -30, -30, -2, -2, 0, 0, 0, 0, 0, 0, 22, 22, 18, 18, 0, 0, 10, 10, -34, -34, 0, 0, -34, -34, -38, -38, 0, 0, 42, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 22, 22, 0, 0, -46, 38, 38, 46, 46, 0, 0, 0, 0, 0, 0, 0, 0, -26, -26, 0, 0, 50, 50, -46, -46, 0, 0, 0, 0, -10, -10, 0, 0, -54, -54, 0, 0, 38, 38, 0, 0, 0, 0, -50, -50, 0, 0, 0, 0, -54, -54, 0, 0, -46, -46, -58, -58, 0, 0, -50, -50, 0, 0, 0, 0, 46, 46, 0, 0, -62, 0, 0, 0, 0, 0, 0, -62, -62] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([2, 2, w])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]