/* 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([-95, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([2, 2, w + 1]) primes_array = [ [2, 2, w + 1],\ [5, 5, -w + 10],\ [7, 7, w + 2],\ [7, 7, w + 5],\ [9, 3, 3],\ [13, 13, w + 2],\ [13, 13, w + 11],\ [19, 19, 2*w - 19],\ [23, 23, w + 7],\ [23, 23, w + 16],\ [31, 31, -w - 8],\ [31, 31, w - 8],\ [37, 37, w + 13],\ [37, 37, w + 24],\ [43, 43, w + 3],\ [43, 43, w + 40],\ [47, 47, w + 1],\ [47, 47, w + 46],\ [53, 53, w + 25],\ [53, 53, w + 28],\ [59, 59, -w - 6],\ [59, 59, w - 6],\ [61, 61, 2*w - 21],\ [61, 61, 6*w - 59],\ [71, 71, 5*w - 48],\ [71, 71, -3*w + 28],\ [79, 79, -w - 4],\ [79, 79, w - 4],\ [83, 83, w + 26],\ [83, 83, w + 57],\ [97, 97, w + 17],\ [97, 97, w + 80],\ [101, 101, -w - 14],\ [101, 101, w - 14],\ [113, 113, w + 35],\ [113, 113, w + 78],\ [121, 11, -11],\ [149, 149, 2*w - 23],\ [149, 149, -2*w - 23],\ [151, 151, 8*w - 77],\ [151, 151, -4*w + 37],\ [163, 163, w + 62],\ [163, 163, w + 101],\ [173, 173, w + 21],\ [173, 173, w + 152],\ [179, 179, 3*w - 26],\ [179, 179, -13*w + 126],\ [193, 193, w + 45],\ [193, 193, w + 148],\ [211, 211, 2*w - 13],\ [211, 211, -2*w - 13],\ [229, 229, -w - 18],\ [229, 229, w - 18],\ [257, 257, w + 98],\ [257, 257, w + 159],\ [263, 263, w + 44],\ [263, 263, w + 219],\ [283, 283, w + 100],\ [283, 283, w + 183],\ [289, 17, -17],\ [293, 293, w + 55],\ [293, 293, w + 238],\ [317, 317, w + 27],\ [317, 317, w + 290],\ [331, 331, 2*w - 7],\ [331, 331, -2*w - 7],\ [337, 337, w + 134],\ [337, 337, w + 203],\ [347, 347, w + 147],\ [347, 347, w + 200],\ [349, 349, 2*w - 27],\ [349, 349, -2*w - 27],\ [367, 367, w + 126],\ [367, 367, w + 241],\ [373, 373, w + 29],\ [373, 373, w + 344],\ [379, 379, 2*w - 1],\ [379, 379, -2*w - 1],\ [389, 389, -w - 22],\ [389, 389, w - 22],\ [431, 431, -4*w - 33],\ [431, 431, 4*w - 33],\ [433, 433, w + 31],\ [433, 433, w + 402],\ [439, 439, 5*w - 44],\ [439, 439, -19*w + 184],\ [443, 443, w + 192],\ [443, 443, w + 251],\ [461, 461, 2*w - 29],\ [461, 461, -2*w - 29],\ [463, 463, w + 133],\ [463, 463, w + 330],\ [467, 467, w + 58],\ [467, 467, w + 409],\ [503, 503, w + 108],\ [503, 503, w + 395],\ [541, 541, 21*w - 206],\ [541, 541, 5*w - 54],\ [587, 587, w + 260],\ [587, 587, w + 327],\ [599, 599, -3*w - 16],\ [599, 599, 3*w - 16],\ [643, 643, w + 122],\ [643, 643, w + 521],\ [647, 647, w + 68],\ [647, 647, w + 579],\ [659, 659, 3*w - 14],\ [659, 659, -3*w - 14],\ [673, 673, w + 257],\ [673, 673, w + 416],\ [677, 677, w + 210],\ [677, 677, w + 467],\ [701, 701, 10*w - 101],\ [701, 701, 14*w - 139],\ [709, 709, 2*w - 33],\ [709, 709, -2*w - 33],\ [727, 727, w + 72],\ [727, 727, w + 655],\ [751, 751, 20*w - 193],\ [751, 751, -8*w + 73],\ [761, 761, -5*w + 56],\ [761, 761, 5*w + 56],\ [769, 769, 17*w - 168],\ [769, 769, 9*w - 92],\ [773, 773, w + 274],\ [773, 773, w + 499],\ [797, 797, w + 172],\ [797, 797, w + 625],\ [809, 809, 8*w - 83],\ [809, 809, 20*w - 197],\ [811, 811, 7*w - 62],\ [811, 811, 7*w + 62],\ [821, 821, -7*w + 74],\ [821, 821, -7*w - 74],\ [823, 823, w + 170],\ [823, 823, w + 653],\ [839, 839, -3*w - 4],\ [839, 839, 3*w - 4],\ [841, 29, -29],\ [857, 857, w + 106],\ [857, 857, w + 751],\ [877, 877, w + 43],\ [877, 877, w + 834],\ [881, 881, 4*w - 49],\ [881, 881, -4*w - 49],\ [883, 883, w + 401],\ [883, 883, w + 482],\ [911, 911, 16*w - 153],\ [911, 911, -12*w + 113],\ [929, 929, -w - 32],\ [929, 929, w - 32],\ [947, 947, w + 82],\ [947, 947, w + 865],\ [953, 953, w + 420],\ [953, 953, w + 533],\ [967, 967, w + 391],\ [967, 967, w + 576],\ [971, 971, 23*w - 222],\ [971, 971, -9*w + 82],\ [977, 977, w + 308],\ [977, 977, w + 669],\ [991, 991, 4*w - 23],\ [991, 991, -4*w - 23]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x^4 + 22*x^2 + 49 K. = NumberField(heckePol) hecke_eigenvalues_array = [1/42*e^3 + 29/42*e, 0, e, 1/7*e^3 + 22/7*e, 1, 1/14*e^3 + 1/14*e, -3/14*e^3 - 59/14*e, -2, 2/7*e^3 + 37/7*e, -1/7*e^3 - 8/7*e, -6, -6, 1/7*e^3 + 1/7*e, -3/7*e^3 - 59/7*e, -2/7*e^3 - 30/7*e, 2/7*e^3 + 30/7*e, -1/7*e^3 - 29/7*e, -1/7*e^3 - 29/7*e, -5/14*e^3 - 61/14*e, 1/2*e^3 + 17/2*e, 1/2*e^2 + 17/2, -1/2*e^2 - 5/2, e^2 + 11, -e^2 - 11, -e^2 - 17, e^2 + 5, -10, -10, 3/7*e^3 + 45/7*e, -3/7*e^3 - 45/7*e, -2*e, -2/7*e^3 - 44/7*e, e^2 + 5, -e^2 - 17, 1/7*e^3 + 29/7*e, 1/7*e^3 + 29/7*e, -6, -e^2 - 5, e^2 + 17, -e^2 - 17, e^2 + 5, -3/7*e^3 - 59/7*e, 1/7*e^3 + 1/7*e, -5/7*e^3 - 61/7*e, e^3 + 17*e, 2*e^2 + 28, -2*e^2 - 16, 3/7*e^3 + 59/7*e, -1/7*e^3 - 1/7*e, -3/2*e^2 - 23/2, 3/2*e^2 + 43/2, -24, -24, -6/7*e^3 - 90/7*e, 6/7*e^3 + 90/7*e, -5/7*e^3 - 61/7*e, e^3 + 17*e, -1/7*e^3 - 15/7*e, 1/7*e^3 + 15/7*e, 7, 5/14*e^3 + 145/14*e, 5/14*e^3 + 145/14*e, 5/14*e^3 + 61/14*e, -1/2*e^3 - 17/2*e, 1/2*e^2 + 41/2, -1/2*e^2 + 19/2, -2/7*e^3 - 2/7*e, 6/7*e^3 + 118/7*e, -12/7*e^3 - 180/7*e, 12/7*e^3 + 180/7*e, 3*e^2 + 43, -3*e^2 - 23, -5/7*e^3 - 89/7*e, 3/7*e^3 + 31/7*e, 1/14*e^3 - 83/14*e, -15/14*e^3 - 323/14*e, 7/2*e^2 + 59/2, -7/2*e^2 - 95/2, -e^2 - 29, e^2 - 7, e^2 - 1, -e^2 - 23, 2/7*e^3 + 30/7*e, -2/7*e^3 - 30/7*e, -3*e^2 - 41, 3*e^2 + 25, 1/7*e^3 + 29/7*e, 1/7*e^3 + 29/7*e, -3*e^2 - 21, 3*e^2 + 45, 1/7*e^3 + 1/7*e, -3/7*e^3 - 59/7*e, 8/7*e^3 + 190/7*e, 2/7*e^3 + 100/7*e, -11/7*e^3 - 214/7*e, 4/7*e^3 + 11/7*e, 20, 20, 11/7*e^3 + 193/7*e, -e^3 - 11*e, 3*e^2 + 33, -3*e^2 - 33, -5/7*e^3 - 117/7*e, -1/7*e^3 - 57/7*e, 4/7*e^3 + 11/7*e, -11/7*e^3 - 214/7*e, -1/2*e^2 - 17/2, 1/2*e^2 + 5/2, 2/7*e^3 + 44/7*e, 2*e, 1/2*e^3 + 17/2*e, -5/14*e^3 - 61/14*e, -2*e^2 - 10, 2*e^2 + 34, -2*e^2 + 14, 2*e^2 + 58, 4/7*e^3 + 39/7*e, -e^3 - 18*e, -e^2 + 19, e^2 + 41, -3, -3, 3*e^2 + 20, -3*e^2 - 46, 3/14*e^3 + 3/14*e, -9/14*e^3 - 177/14*e, -15/14*e^3 - 183/14*e, 3/2*e^3 + 51/2*e, -2*e^2 - 25, 2*e^2 + 19, -3/2*e^2 - 91/2, 3/2*e^2 - 25/2, 2*e^2 + 4, -2*e^2 - 40, -6/7*e^3 - 167/7*e, -5/7*e^3 - 152/7*e, -3*e^2 - 57, 3*e^2 + 9, -39, -8/7*e^3 - 148/7*e, 4/7*e^3 + 32/7*e, -17/14*e^3 - 269/14*e, 15/14*e^3 + 211/14*e, 2*e^2 + 52, -2*e^2 + 8, -8*e, -8/7*e^3 - 176/7*e, e^2 - 1, -e^2 - 23, 4*e^2 + 35, -4*e^2 - 53, 11/7*e^3 + 277/7*e, 5/7*e^3 + 187/7*e, -8/7*e^3 - 64/7*e, 16/7*e^3 + 296/7*e, 11/7*e^3 + 179/7*e, -9/7*e^3 - 121/7*e, -2*e^2 - 52, 2*e^2 - 8, -4/7*e^3 - 74/7*e, 2/7*e^3 + 16/7*e, -20, -20] 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])] = -1/42*e^3 - 29/42*e # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]