/* 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([-38, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([38, 38, w]) primes_array = [ [2, 2, w - 6],\ [9, 3, 3],\ [11, 11, -w + 7],\ [11, 11, w + 7],\ [13, 13, -w - 5],\ [13, 13, w - 5],\ [17, 17, -2*w + 13],\ [17, 17, -2*w - 13],\ [19, 19, -3*w + 19],\ [25, 5, 5],\ [29, 29, -w - 3],\ [29, 29, w - 3],\ [31, 31, -2*w + 11],\ [31, 31, -8*w + 49],\ [37, 37, -w - 1],\ [37, 37, w - 1],\ [43, 43, -w - 9],\ [43, 43, w - 9],\ [49, 7, -7],\ [53, 53, -3*w + 17],\ [53, 53, -9*w + 55],\ [71, 71, 2*w - 9],\ [71, 71, -2*w - 9],\ [73, 73, 2*w - 15],\ [73, 73, -2*w - 15],\ [79, 79, -4*w + 23],\ [79, 79, -10*w + 61],\ [83, 83, -w - 11],\ [83, 83, w - 11],\ [103, 103, 2*w - 7],\ [103, 103, -2*w - 7],\ [109, 109, -5*w + 29],\ [109, 109, -11*w + 67],\ [127, 127, 2*w - 5],\ [127, 127, -2*w - 5],\ [131, 131, -w - 13],\ [131, 131, w - 13],\ [137, 137, 2*w - 17],\ [137, 137, -2*w - 17],\ [139, 139, 5*w - 33],\ [139, 139, -13*w + 81],\ [151, 151, 2*w - 1],\ [151, 151, -2*w - 1],\ [163, 163, -11*w + 69],\ [163, 163, 7*w - 45],\ [167, 167, 4*w + 21],\ [167, 167, -4*w + 21],\ [173, 173, -3*w - 13],\ [173, 173, 3*w - 13],\ [181, 181, -7*w + 41],\ [181, 181, -13*w + 79],\ [223, 223, -8*w + 47],\ [223, 223, -14*w + 85],\ [233, 233, 4*w - 29],\ [233, 233, -4*w - 29],\ [251, 251, -w - 17],\ [251, 251, w - 17],\ [269, 269, -9*w + 53],\ [269, 269, -15*w + 91],\ [283, 283, 3*w - 25],\ [283, 283, -3*w - 25],\ [293, 293, -3*w - 7],\ [293, 293, 3*w - 7],\ [313, 313, -24*w + 149],\ [313, 313, 6*w - 41],\ [317, 317, 3*w - 5],\ [317, 317, -3*w - 5],\ [347, 347, 7*w - 47],\ [347, 347, -23*w + 143],\ [353, 353, -4*w - 31],\ [353, 353, 4*w - 31],\ [373, 373, -11*w + 65],\ [373, 373, -17*w + 103],\ [383, 383, 4*w - 15],\ [383, 383, -4*w - 15],\ [419, 419, 37*w - 229],\ [419, 419, -5*w + 37],\ [421, 421, -5*w - 23],\ [421, 421, 5*w - 23],\ [431, 431, -12*w + 71],\ [431, 431, -18*w + 109],\ [439, 439, -4*w - 13],\ [439, 439, 4*w - 13],\ [443, 443, -19*w + 119],\ [443, 443, 11*w - 71],\ [457, 457, 12*w - 77],\ [457, 457, -18*w + 113],\ [467, 467, -17*w + 107],\ [467, 467, 13*w - 83],\ [487, 487, 4*w - 11],\ [487, 487, -4*w - 11],\ [491, 491, -w - 23],\ [491, 491, w - 23],\ [499, 499, -3*w - 29],\ [499, 499, 3*w - 29],\ [509, 509, -5*w - 21],\ [509, 509, 5*w - 21],\ [529, 23, -23],\ [571, 571, -5*w - 39],\ [571, 571, 5*w - 39],\ [577, 577, 2*w - 27],\ [577, 577, -2*w - 27],\ [587, 587, -w - 25],\ [587, 587, w - 25],\ [593, 593, -34*w + 211],\ [593, 593, 8*w - 55],\ [599, 599, 4*w - 3],\ [599, 599, -4*w - 3],\ [607, 607, -4*w - 1],\ [607, 607, 4*w - 1],\ [617, 617, -4*w - 35],\ [617, 617, 4*w - 35],\ [619, 619, 3*w - 31],\ [619, 619, -3*w - 31],\ [643, 643, 9*w - 61],\ [643, 643, -33*w + 205],\ [661, 661, 5*w - 17],\ [661, 661, -5*w - 17],\ [677, 677, -9*w + 49],\ [677, 677, -39*w + 239],\ [691, 691, -w - 27],\ [691, 691, w - 27],\ [739, 739, 47*w - 291],\ [739, 739, -7*w + 51],\ [743, 743, -6*w - 25],\ [743, 743, 6*w - 25],\ [751, 751, -50*w + 307],\ [751, 751, -8*w + 41],\ [761, 761, 4*w - 37],\ [761, 761, -4*w - 37],\ [769, 769, -30*w + 187],\ [769, 769, 12*w - 79],\ [773, 773, -7*w - 33],\ [773, 773, 7*w - 33],\ [797, 797, -31*w + 189],\ [797, 797, -13*w + 75],\ [809, 809, 2*w - 31],\ [809, 809, -2*w - 31],\ [829, 829, -5*w - 11],\ [829, 829, 5*w - 11],\ [839, 839, 6*w - 23],\ [839, 839, -6*w - 23],\ [859, 859, -27*w + 169],\ [859, 859, 15*w - 97],\ [863, 863, -18*w + 107],\ [863, 863, -24*w + 145],\ [877, 877, -41*w + 251],\ [877, 877, -11*w + 61],\ [881, 881, 16*w - 103],\ [881, 881, -26*w + 163],\ [883, 883, -3*w - 35],\ [883, 883, 3*w - 35],\ [887, 887, -14*w + 81],\ [887, 887, -32*w + 195],\ [911, 911, 8*w - 39],\ [911, 911, -8*w - 39],\ [929, 929, 20*w - 127],\ [929, 929, -22*w + 139],\ [937, 937, 2*w - 33],\ [937, 937, -2*w - 33],\ [941, 941, -5*w - 3],\ [941, 941, 5*w - 3],\ [947, 947, 7*w - 53],\ [947, 947, -7*w - 53],\ [983, 983, -12*w + 67],\ [983, 983, -42*w + 257],\ [991, 991, -10*w + 53],\ [991, 991, 10*w + 53]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -5, 2, 2, 1, 1, 3, 3, -1, 6, 5, 5, 8, 8, 2, 2, 4, 4, -5, 1, 1, -2, -2, 9, 9, 10, 10, -6, -6, 6, 6, 15, 15, -18, -18, 12, 12, -17, -17, 0, 0, -2, -2, -16, -16, 12, 12, 6, 6, -22, -22, -14, -14, -6, -6, 2, 2, -30, -30, -6, -6, -9, -9, 29, 29, 27, 27, -2, -2, 9, 9, -29, -29, 26, 26, 0, 0, 13, 13, 18, 18, -20, -20, -26, -26, -7, -7, -2, -2, 2, 2, -28, -28, 40, 40, 30, 30, -45, -28, -28, -37, -37, -12, -12, 34, 34, 0, 0, 22, 22, 18, 18, 10, 10, -26, -26, 23, 23, -13, -13, 42, 42, -40, -40, 16, 16, -32, -32, 27, 27, -35, -35, -9, -9, -3, -3, -15, -15, 15, 15, -20, -20, -50, -50, -54, -54, -13, -13, -18, -18, 34, 34, 2, 2, -12, -12, -55, -55, -7, -7, -7, -7, -12, -12, 6, 6, 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([2, 2, w - 6])] = 1 AL_eigenvalues[ZF.ideal([19, 19, -3*w + 19])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]