/* 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([-33, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([28, 14, 6*w - 38]) primes_array = [ [3, 3, -w + 6],\ [3, 3, -w - 5],\ [4, 2, 2],\ [7, 7, 3*w - 19],\ [11, 11, -2*w - 11],\ [11, 11, -2*w + 13],\ [13, 13, w + 4],\ [13, 13, -w + 5],\ [19, 19, 5*w - 31],\ [23, 23, -w - 7],\ [23, 23, w - 8],\ [25, 5, -5],\ [31, 31, -w - 1],\ [31, 31, w - 2],\ [41, 41, 6*w + 31],\ [41, 41, 6*w - 37],\ [43, 43, -3*w - 17],\ [43, 43, -3*w + 20],\ [59, 59, 3*w - 17],\ [59, 59, 3*w + 14],\ [89, 89, 3*w + 13],\ [89, 89, 3*w - 16],\ [97, 97, 2*w - 7],\ [97, 97, -2*w - 5],\ [103, 103, 8*w + 41],\ [103, 103, 8*w - 49],\ [137, 137, 11*w - 70],\ [137, 137, 11*w + 59],\ [149, 149, -w - 13],\ [149, 149, w - 14],\ [163, 163, -3*w - 20],\ [163, 163, 3*w - 23],\ [167, 167, -3*w - 10],\ [167, 167, 3*w - 13],\ [173, 173, 6*w - 35],\ [173, 173, 6*w + 29],\ [181, 181, 5*w + 23],\ [181, 181, 5*w - 28],\ [191, 191, 2*w - 19],\ [191, 191, -2*w - 17],\ [197, 197, 4*w - 29],\ [197, 197, -4*w - 25],\ [223, 223, 7*w - 41],\ [223, 223, 7*w + 34],\ [227, 227, -3*w - 7],\ [227, 227, 3*w - 10],\ [233, 233, 13*w + 70],\ [233, 233, 13*w - 83],\ [239, 239, -w - 16],\ [239, 239, w - 17],\ [241, 241, 11*w + 56],\ [241, 241, 11*w - 67],\ [257, 257, 3*w - 8],\ [257, 257, -3*w - 5],\ [263, 263, -7*w + 47],\ [263, 263, -7*w - 40],\ [269, 269, -3*w - 4],\ [269, 269, 3*w - 7],\ [277, 277, 9*w - 59],\ [277, 277, -9*w - 50],\ [289, 17, -17],\ [293, 293, -3*w - 1],\ [293, 293, 3*w - 4],\ [307, 307, -4*w - 13],\ [307, 307, 4*w - 17],\ [347, 347, -w - 19],\ [347, 347, w - 20],\ [359, 359, 5*w + 32],\ [359, 359, -5*w + 37],\ [383, 383, 21*w - 130],\ [383, 383, 24*w - 149],\ [389, 389, -20*w + 127],\ [389, 389, 25*w - 158],\ [409, 409, 10*w - 59],\ [409, 409, 10*w + 49],\ [433, 433, 14*w + 71],\ [433, 433, 14*w - 85],\ [439, 439, -7*w + 38],\ [439, 439, 7*w + 31],\ [443, 443, 2*w - 25],\ [443, 443, -2*w - 23],\ [457, 457, -3*w - 26],\ [457, 457, 3*w - 29],\ [463, 463, 18*w + 97],\ [463, 463, 18*w - 115],\ [491, 491, 17*w - 109],\ [491, 491, 17*w + 92],\ [499, 499, -9*w + 61],\ [499, 499, -9*w - 52],\ [509, 509, 15*w + 76],\ [509, 509, 15*w - 91],\ [521, 521, 6*w - 29],\ [521, 521, -6*w - 23],\ [523, 523, -4*w - 1],\ [523, 523, 4*w - 5],\ [541, 541, -12*w - 67],\ [541, 541, 12*w - 79],\ [557, 557, -4*w - 31],\ [557, 557, 4*w - 35],\ [563, 563, 12*w - 71],\ [563, 563, 12*w + 59],\ [571, 571, 3*w - 31],\ [571, 571, -3*w - 28],\ [601, 601, 11*w + 53],\ [601, 601, 11*w - 64],\ [607, 607, 8*w + 35],\ [607, 607, -8*w + 43],\ [613, 613, -9*w - 53],\ [613, 613, -9*w + 62],\ [617, 617, -w - 25],\ [617, 617, w - 26],\ [631, 631, -3*w - 29],\ [631, 631, 3*w - 32],\ [653, 653, 19*w + 103],\ [653, 653, 19*w - 122],\ [661, 661, 19*w - 116],\ [661, 661, 19*w + 97],\ [677, 677, 33*w - 205],\ [677, 677, 33*w + 172],\ [701, 701, -13*w + 86],\ [701, 701, -13*w - 73],\ [709, 709, 15*w - 98],\ [709, 709, -15*w - 83],\ [739, 739, -6*w - 41],\ [739, 739, 6*w - 47],\ [757, 757, 3*w - 34],\ [757, 757, -3*w - 31],\ [773, 773, 18*w + 91],\ [773, 773, 18*w - 109],\ [787, 787, 28*w - 173],\ [787, 787, -37*w + 230],\ [797, 797, 6*w - 23],\ [797, 797, -6*w - 17],\ [809, 809, 5*w - 43],\ [809, 809, -5*w - 38],\ [811, 811, 5*w - 7],\ [811, 811, -5*w - 2],\ [821, 821, 7*w - 53],\ [821, 821, 7*w + 46],\ [823, 823, -3*w - 32],\ [823, 823, 3*w - 35],\ [829, 829, 5*w - 4],\ [829, 829, 5*w - 1],\ [839, 839, 15*w - 89],\ [839, 839, 15*w + 74],\ [841, 29, -29],\ [857, 857, 21*w - 128],\ [857, 857, 21*w + 107],\ [883, 883, 27*w + 145],\ [883, 883, 27*w - 172],\ [887, 887, 9*w - 47],\ [887, 887, -9*w - 38],\ [919, 919, 6*w - 49],\ [919, 919, -6*w - 43],\ [941, 941, -6*w - 13],\ [941, 941, 6*w - 19],\ [947, 947, -11*w - 65],\ [947, 947, -11*w + 76],\ [967, 967, -9*w - 56],\ [967, 967, 9*w - 65],\ [971, 971, 9*w + 37],\ [971, 971, 9*w - 46],\ [983, 983, 27*w + 139],\ [983, 983, 27*w - 166]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, 1, 1, 0, 0, -4, -4, 2, 0, 0, -10, -4, -4, 6, 6, 8, 8, -6, -6, -6, -6, -10, -10, -4, -4, 18, 18, -18, -18, -16, -16, -12, -12, -12, -12, 20, 20, 24, 24, -18, -18, 8, 8, 18, 18, -6, -6, 24, 24, -10, -10, 18, 18, 0, 0, -12, -12, -10, -10, 2, 24, 24, 2, 2, -24, -24, -24, -24, 36, 36, 18, 18, 14, 14, -34, -34, 8, 8, -12, -12, -10, -10, 32, 32, -12, -12, -4, -4, 36, 36, 6, 6, 2, 2, 38, 38, 6, 6, 30, 30, 32, 32, 26, 26, 32, 32, 2, 2, 6, 6, -16, -16, 18, 18, -40, -40, -12, -12, 18, 18, -46, -46, -16, -16, 2, 2, 24, 24, -22, -22, -12, -12, 6, 6, 2, 2, 6, 6, -40, -40, 56, 56, 12, 12, -22, -18, -18, 20, 20, -36, -36, 56, 56, -24, -24, 24, 24, 32, 32, -6, -6, -36, -36] 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, 3*w - 19])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]