/* 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([-17, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([92, 46, -6*w + 26]) primes_array = [ [3, 3, w - 5],\ [4, 2, 2],\ [5, 5, -w + 4],\ [5, 5, -w - 3],\ [11, 11, w + 2],\ [11, 11, -w + 3],\ [13, 13, w + 5],\ [13, 13, -w + 6],\ [17, 17, -w],\ [17, 17, w - 1],\ [23, 23, -3*w + 13],\ [31, 31, 2*w - 11],\ [31, 31, -5*w + 24],\ [49, 7, -7],\ [53, 53, 2*w - 5],\ [53, 53, -2*w - 3],\ [73, 73, -w - 9],\ [73, 73, w - 10],\ [83, 83, -3*w - 7],\ [83, 83, 3*w - 10],\ [89, 89, -7*w + 31],\ [89, 89, 5*w - 21],\ [107, 107, 4*w - 15],\ [107, 107, 4*w + 11],\ [113, 113, 3*w - 8],\ [113, 113, -3*w - 5],\ [127, 127, 2*w - 15],\ [127, 127, -2*w - 13],\ [137, 137, -9*w + 40],\ [137, 137, 6*w - 25],\ [139, 139, -w - 12],\ [139, 139, w - 13],\ [149, 149, -3*w - 1],\ [149, 149, 3*w - 4],\ [151, 151, 3*w - 19],\ [151, 151, -3*w - 16],\ [163, 163, -6*w + 31],\ [163, 163, -9*w + 44],\ [191, 191, -5*w - 13],\ [191, 191, 5*w - 18],\ [193, 193, -w - 14],\ [193, 193, w - 15],\ [211, 211, -7*w + 36],\ [211, 211, -10*w + 49],\ [223, 223, -w - 15],\ [223, 223, w - 16],\ [227, 227, -4*w - 5],\ [227, 227, 4*w - 9],\ [251, 251, 4*w - 7],\ [251, 251, -4*w - 3],\ [263, 263, -13*w + 58],\ [263, 263, 8*w - 33],\ [271, 271, -17*w + 81],\ [271, 271, -5*w + 29],\ [277, 277, -13*w + 63],\ [277, 277, -7*w + 37],\ [281, 281, -10*w + 43],\ [281, 281, -11*w + 48],\ [293, 293, 7*w - 27],\ [293, 293, 7*w + 20],\ [307, 307, -3*w - 20],\ [307, 307, 3*w - 23],\ [331, 331, 2*w - 21],\ [331, 331, -2*w - 19],\ [349, 349, -4*w - 23],\ [349, 349, 4*w - 27],\ [359, 359, -5*w - 6],\ [359, 359, 5*w - 11],\ [361, 19, -19],\ [383, 383, -7*w - 18],\ [383, 383, 7*w - 25],\ [389, 389, 5*w - 9],\ [389, 389, -5*w - 4],\ [397, 397, 3*w - 25],\ [397, 397, -3*w - 22],\ [401, 401, -5*w - 3],\ [401, 401, 5*w - 8],\ [409, 409, -15*w + 73],\ [409, 409, -9*w + 47],\ [419, 419, -5*w - 1],\ [419, 419, 5*w - 6],\ [431, 431, 5*w - 2],\ [431, 431, 5*w - 3],\ [439, 439, -5*w - 27],\ [439, 439, 5*w - 32],\ [463, 463, -11*w + 56],\ [463, 463, -14*w + 69],\ [467, 467, 9*w - 35],\ [467, 467, 9*w + 26],\ [479, 479, 8*w - 29],\ [479, 479, -8*w - 21],\ [487, 487, -7*w + 40],\ [487, 487, -22*w + 105],\ [499, 499, 5*w - 33],\ [499, 499, -5*w - 28],\ [503, 503, -7*w - 15],\ [503, 503, 7*w - 22],\ [521, 521, -6*w - 7],\ [521, 521, 6*w - 13],\ [541, 541, -12*w + 61],\ [541, 541, -15*w + 74],\ [547, 547, 3*w - 28],\ [547, 547, -3*w - 25],\ [557, 557, 6*w - 11],\ [557, 557, -6*w - 5],\ [563, 563, 13*w - 55],\ [563, 563, -17*w + 75],\ [569, 569, 10*w - 39],\ [569, 569, 10*w + 29],\ [577, 577, -23*w + 110],\ [577, 577, 8*w - 45],\ [601, 601, -3*w - 26],\ [601, 601, 3*w - 29],\ [607, 607, 2*w - 27],\ [607, 607, -2*w - 25],\ [617, 617, 6*w - 5],\ [617, 617, 6*w - 1],\ [641, 641, -9*w - 23],\ [641, 641, 9*w - 32],\ [659, 659, 13*w - 54],\ [659, 659, -20*w + 89],\ [673, 673, 9*w - 50],\ [673, 673, -24*w + 115],\ [677, 677, -19*w + 84],\ [677, 677, 14*w - 59],\ [691, 691, 5*w - 36],\ [691, 691, -5*w - 31],\ [701, 701, 10*w + 27],\ [701, 701, 10*w - 37],\ [739, 739, -w - 27],\ [739, 739, w - 28],\ [743, 743, 8*w - 23],\ [743, 743, -8*w - 15],\ [773, 773, -7*w - 5],\ [773, 773, 7*w - 12],\ [797, 797, 9*w - 29],\ [797, 797, -9*w - 20],\ [811, 811, -15*w + 76],\ [811, 811, -18*w + 89],\ [823, 823, -6*w - 35],\ [823, 823, 6*w - 41],\ [827, 827, 11*w - 41],\ [827, 827, 11*w + 30],\ [829, 829, 5*w - 38],\ [829, 829, -5*w - 33],\ [839, 839, 7*w - 6],\ [839, 839, 7*w - 1],\ [841, 29, -29],\ [853, 853, -w - 29],\ [853, 853, w - 30],\ [859, 859, -9*w + 52],\ [859, 859, -30*w + 143],\ [877, 877, -7*w - 38],\ [877, 877, 7*w - 45],\ [881, 881, -25*w + 112],\ [881, 881, 14*w - 57],\ [883, 883, -26*w + 125],\ [883, 883, 11*w - 60],\ [911, 911, 15*w - 62],\ [911, 911, -24*w + 107],\ [941, 941, 10*w - 33],\ [941, 941, -10*w - 23],\ [953, 953, 17*w - 72],\ [953, 953, -22*w + 97],\ [967, 967, -3*w - 32],\ [967, 967, 3*w - 35],\ [971, 971, -19*w + 82],\ [971, 971, -20*w + 87],\ [977, 977, -9*w - 16],\ [977, 977, 9*w - 25],\ [983, 983, 8*w - 15],\ [983, 983, -8*w - 7],\ [991, 991, -25*w + 121],\ [991, 991, -13*w + 69],\ [997, 997, 12*w - 65],\ [997, 997, -27*w + 130]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, 1, 4, 4, 2, 2, -2, -2, -2, -2, 1, 0, 0, 2, -4, -4, 6, 6, 14, 14, -6, -6, -10, -10, -14, -14, 16, 16, 6, 6, -4, -4, -4, -4, -8, -8, -8, -8, 20, 20, 26, 26, -20, -20, -16, -16, -6, -6, 14, 14, -16, -16, 8, 8, -14, -14, -6, -6, 4, 4, -16, -16, -4, -4, 26, 26, -12, -12, -34, -24, -24, 0, 0, 14, 14, -18, -18, 34, 34, -18, -18, -12, -12, 8, 8, 40, 40, -2, -2, -8, -8, -8, -8, 16, 16, 12, 12, 38, 38, -6, -6, -36, -36, 16, 16, -14, -14, 14, 14, 30, 30, -26, -26, 32, 32, 18, 18, 14, 14, 30, 30, -2, -2, -12, -12, -4, -4, 0, 0, -32, -32, -24, -24, -40, -40, 8, 8, 20, 20, 24, 24, 6, 6, -30, -30, 24, 24, -54, 46, 46, 40, 40, 18, 18, 18, 18, -36, -36, 20, 20, 36, 36, 46, 46, -16, -16, -38, -38, 6, 6, -36, -36, -56, -56, 10, 10] 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([23, 23, -3*w + 13])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]