/* 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([-75, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([28, 14, -46*w - 376]) primes_array = [ [3, 3, w - 9],\ [3, 3, w + 8],\ [4, 2, 2],\ [5, 5, -6*w + 55],\ [5, 5, -6*w - 49],\ [7, 7, -23*w - 188],\ [11, 11, 5*w - 46],\ [11, 11, -5*w - 41],\ [19, 19, w + 7],\ [19, 19, -w + 8],\ [23, 23, 2*w - 19],\ [23, 23, 2*w + 17],\ [43, 43, 57*w - 523],\ [53, 53, 28*w - 257],\ [53, 53, 28*w + 229],\ [61, 61, -13*w + 119],\ [61, 61, 13*w + 106],\ [67, 67, -9*w + 83],\ [67, 67, -9*w - 74],\ [73, 73, -w - 1],\ [73, 73, w - 2],\ [79, 79, 3*w + 26],\ [79, 79, 3*w - 29],\ [89, 89, -9*w - 73],\ [89, 89, -9*w + 82],\ [107, 107, -w - 13],\ [107, 107, w - 14],\ [109, 109, 45*w - 413],\ [109, 109, -45*w - 368],\ [127, 127, 39*w + 319],\ [127, 127, 39*w - 358],\ [131, 131, 132*w + 1079],\ [131, 131, 75*w + 613],\ [157, 157, 2*w - 13],\ [157, 157, -2*w - 11],\ [169, 13, -13],\ [193, 193, -3*w + 31],\ [193, 193, -3*w - 28],\ [197, 197, -w - 16],\ [197, 197, w - 17],\ [199, 199, 235*w + 1921],\ [199, 199, 64*w + 523],\ [223, 223, -31*w + 284],\ [223, 223, 31*w + 253],\ [227, 227, -12*w - 97],\ [227, 227, -12*w + 109],\ [239, 239, -38*w + 349],\ [239, 239, -38*w - 311],\ [241, 241, -5*w - 38],\ [241, 241, -5*w + 43],\ [257, 257, -3*w - 19],\ [257, 257, 3*w - 22],\ [281, 281, 5*w + 44],\ [281, 281, 5*w - 49],\ [289, 17, -17],\ [313, 313, 59*w + 482],\ [313, 313, 59*w - 541],\ [317, 317, -4*w + 41],\ [317, 317, -4*w - 37],\ [337, 337, 24*w - 221],\ [337, 337, 24*w + 197],\ [349, 349, -14*w - 113],\ [349, 349, -14*w + 127],\ [359, 359, -125*w - 1022],\ [359, 359, 125*w - 1147],\ [379, 379, 3*w - 34],\ [379, 379, -3*w - 31],\ [383, 383, 201*w + 1643],\ [383, 383, 144*w + 1177],\ [401, 401, -11*w + 103],\ [401, 401, 11*w + 92],\ [409, 409, 110*w + 899],\ [409, 409, 110*w - 1009],\ [419, 419, -15*w - 121],\ [419, 419, -15*w + 136],\ [431, 431, -w - 22],\ [431, 431, w - 23],\ [433, 433, -19*w + 173],\ [433, 433, -19*w - 154],\ [443, 443, -22*w + 203],\ [443, 443, -22*w - 181],\ [467, 467, -3*w - 13],\ [467, 467, 3*w - 16],\ [487, 487, -21*w - 173],\ [487, 487, -21*w + 194],\ [503, 503, 99*w + 809],\ [503, 503, 99*w - 908],\ [521, 521, 3*w - 14],\ [521, 521, -3*w - 11],\ [523, 523, 44*w + 359],\ [523, 523, 44*w - 403],\ [541, 541, 60*w - 551],\ [541, 541, -60*w - 491],\ [547, 547, 9*w - 86],\ [547, 547, 9*w + 77],\ [557, 557, -19*w + 176],\ [557, 557, -19*w - 157],\ [569, 569, 5*w + 47],\ [569, 569, -5*w + 52],\ [577, 577, -17*w - 137],\ [577, 577, -17*w + 154],\ [587, 587, 3*w - 11],\ [587, 587, -3*w - 8],\ [593, 593, -6*w - 43],\ [593, 593, -6*w + 49],\ [599, 599, 2*w - 31],\ [599, 599, -2*w - 29],\ [601, 601, 77*w + 629],\ [601, 601, 77*w - 706],\ [607, 607, -7*w + 59],\ [607, 607, -7*w - 52],\ [613, 613, 12*w - 113],\ [613, 613, 12*w + 101],\ [617, 617, -16*w - 133],\ [617, 617, -16*w + 149],\ [647, 647, -3*w - 4],\ [647, 647, 3*w - 7],\ [659, 659, -383*w - 3131],\ [659, 659, -130*w - 1063],\ [677, 677, 3*w - 2],\ [677, 677, 3*w - 1],\ [683, 683, -53*w + 487],\ [683, 683, -53*w - 434],\ [691, 691, 5*w - 37],\ [691, 691, -5*w - 32],\ [701, 701, 89*w - 817],\ [701, 701, 89*w + 728],\ [709, 709, -33*w - 271],\ [709, 709, -33*w + 304],\ [727, 727, -13*w + 116],\ [727, 727, -13*w - 103],\ [733, 733, -11*w - 86],\ [733, 733, -11*w + 97],\ [761, 761, 270*w + 2207],\ [761, 761, 213*w + 1741],\ [773, 773, 6*w - 47],\ [773, 773, -6*w - 41],\ [809, 809, 8*w + 71],\ [809, 809, 8*w - 79],\ [811, 811, -100*w + 917],\ [811, 811, 100*w + 817],\ [821, 821, -4*w - 43],\ [821, 821, 4*w - 47],\ [823, 823, -423*w - 3458],\ [823, 823, -147*w - 1202],\ [827, 827, 199*w - 1826],\ [827, 827, -199*w - 1627],\ [829, 829, 179*w + 1463],\ [829, 829, 179*w - 1642],\ [839, 839, -9*w - 68],\ [839, 839, -9*w + 77],\ [841, 29, -29],\ [859, 859, -20*w - 161],\ [859, 859, -20*w + 181],\ [877, 877, 9*w - 88],\ [877, 877, 9*w + 79],\ [883, 883, -3*w - 38],\ [883, 883, 3*w - 41],\ [887, 887, -117*w - 956],\ [887, 887, 117*w - 1073],\ [907, 907, -141*w - 1153],\ [907, 907, 141*w - 1294],\ [919, 919, -30*w + 277],\ [919, 919, -30*w - 247],\ [929, 929, -15*w + 134],\ [929, 929, -15*w - 119],\ [937, 937, -37*w - 301],\ [937, 937, -37*w + 338],\ [947, 947, 94*w + 769],\ [947, 947, 94*w - 863],\ [961, 31, -31],\ [967, 967, -51*w - 418],\ [967, 967, -51*w + 469],\ [977, 977, -29*w - 239],\ [977, 977, -29*w + 268],\ [983, 983, -9*w + 76],\ [983, 983, -9*w - 67],\ [997, 997, 202*w - 1853],\ [997, 997, 202*w + 1651]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, 1, 0, 0, 1, 0, 0, 2, 2, 0, 0, 8, 6, 6, 8, 8, -4, -4, 2, 2, 8, 8, -6, -6, 12, 12, 2, 2, -16, -16, 18, 18, -4, -4, -10, 14, 14, -18, -18, 20, 20, 8, 8, 18, 18, 24, 24, -10, -10, 18, 18, -6, -6, 2, -10, -10, 6, 6, 14, 14, -28, -28, -24, -24, -16, -16, 36, 36, -18, -18, 14, 14, 6, 6, 24, 24, -34, -34, -12, -12, -6, -6, -16, -16, 0, 0, 6, 6, 2, 2, 38, 38, 8, 8, 6, 6, 6, 6, 2, 2, -42, -42, -6, -6, -24, -24, 26, 26, 32, 32, 2, 2, 6, 6, -12, -12, -24, -24, -12, -12, -12, -12, -46, -46, 18, 18, -46, -46, 44, 44, -40, -40, -18, -18, 24, 24, 6, 6, 2, 2, 6, 6, -40, -40, -36, -36, 56, 56, 12, 12, -22, 14, 14, -22, -22, 20, 20, -36, -36, 44, 44, 56, 56, 6, 6, 2, 2, 24, 24, -46, 32, 32, -6, -6, -36, -36, 8, 8] 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([7, 7, -23*w - 188])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]