/* 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([-5, -9, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 4, -2*w - 2]) primes_array = [ [2, 2, -w - 1],\ [5, 5, w],\ [7, 7, w^2 - 2*w - 8],\ [7, 7, -2*w^2 + 3*w + 16],\ [7, 7, -w^2 + 2*w + 6],\ [11, 11, w^2 - 2*w - 2],\ [19, 19, -w + 2],\ [23, 23, -w^2 + 3*w + 1],\ [25, 5, w^2 - w - 9],\ [27, 3, 3],\ [29, 29, -w^2 - w + 1],\ [29, 29, w^2 - 2*w - 4],\ [29, 29, -w^2 + w + 11],\ [43, 43, 2*w^2 - 3*w - 18],\ [47, 47, -2*w + 7],\ [53, 53, w^2 - w - 3],\ [61, 61, w^2 + 2*w + 2],\ [67, 67, -2*w^2 + 5*w + 8],\ [79, 79, w^2 - 3*w - 9],\ [97, 97, -w^2 - 2*w + 2],\ [109, 109, -2*w^2 + 4*w + 11],\ [109, 109, -3*w^2 + 4*w + 26],\ [109, 109, -3*w^2 + 4*w + 28],\ [113, 113, -4*w^2 + 8*w + 27],\ [121, 11, 5*w^2 - 8*w - 38],\ [127, 127, -3*w^2 + 4*w + 24],\ [131, 131, -4*w^2 + 5*w + 38],\ [139, 139, 2*w - 3],\ [149, 149, -w^2 + 3*w - 1],\ [151, 151, w^2 - 4*w - 6],\ [157, 157, 2*w^2 - 3*w - 12],\ [167, 167, -3*w^2 + 6*w + 22],\ [173, 173, -3*w^2 + 8*w + 8],\ [181, 181, w^2 - 2*w - 12],\ [181, 181, w^2 - 12],\ [181, 181, -4*w - 1],\ [191, 191, 2*w^2 - 6*w - 9],\ [193, 193, -8*w^2 + 12*w + 67],\ [197, 197, 2*w^2 - 3*w - 4],\ [199, 199, 2*w^2 - 2*w - 11],\ [211, 211, 4*w^2 - 6*w - 29],\ [223, 223, 3*w^2 - 5*w - 27],\ [227, 227, -4*w^2 + 7*w + 28],\ [229, 229, 3*w^2 - 8*w - 14],\ [229, 229, w^2 - 4*w - 8],\ [229, 229, -2*w - 7],\ [233, 233, -5*w^2 + 7*w + 43],\ [241, 241, 2*w^2 - 4*w - 7],\ [251, 251, w^2 + 2],\ [251, 251, -2*w^2 + 2*w + 1],\ [251, 251, 2*w^2 - 5*w - 2],\ [263, 263, 2*w^2 - 5*w - 14],\ [269, 269, -w^2 + 5*w - 1],\ [271, 271, -2*w^2 - w + 2],\ [277, 277, -3*w^2 + 7*w + 7],\ [281, 281, -5*w^2 + 10*w + 34],\ [293, 293, -2*w^2 + 5*w + 16],\ [311, 311, w^2 + w + 3],\ [313, 313, 2*w^2 + w - 4],\ [317, 317, -7*w^2 + 13*w + 49],\ [331, 331, w^2 - 5*w - 7],\ [337, 337, -w^2 + 2*w - 2],\ [337, 337, 7*w^2 - 12*w - 52],\ [337, 337, -2*w^2 + 3],\ [347, 347, -10*w^2 + 17*w + 76],\ [349, 349, 2*w^2 - 2*w - 9],\ [353, 353, 2*w^2 - 3*w - 8],\ [359, 359, -4*w^2 + 5*w + 36],\ [361, 19, w^2 + w - 7],\ [367, 367, -4*w^2 + 8*w + 29],\ [373, 373, 2*w^2 - 6*w - 11],\ [373, 373, 8*w^2 - 14*w - 59],\ [379, 379, -2*w^2 + w + 4],\ [383, 383, -3*w^2 + 2*w + 34],\ [383, 383, 5*w^2 - 7*w - 41],\ [383, 383, 3*w^2 - 7*w - 19],\ [397, 397, -7*w^2 + 13*w + 51],\ [431, 431, -8*w^2 + 14*w + 63],\ [433, 433, -2*w^2 + 9*w + 8],\ [443, 443, -6*w^2 + 10*w + 51],\ [443, 443, 3*w - 4],\ [443, 443, w^2 - 7*w - 3],\ [449, 449, -7*w^2 + 10*w + 62],\ [461, 461, -6*w^2 + 11*w + 46],\ [461, 461, 2*w^2 - 4*w - 1],\ [461, 461, w^2 - 5*w - 9],\ [463, 463, 7*w + 6],\ [463, 463, -5*w^2 + 8*w + 36],\ [463, 463, 3*w^2 - 2*w - 16],\ [467, 467, 3*w^2 - 7*w - 9],\ [467, 467, 4*w - 1],\ [467, 467, 6*w^2 - 11*w - 48],\ [479, 479, 2*w^2 - 4*w - 21],\ [479, 479, w^2 + 7*w + 7],\ [479, 479, w^2 - 2*w - 14],\ [487, 487, w^2 - 5*w - 11],\ [487, 487, 3*w^2 - 3*w - 23],\ [487, 487, w^2 + 3*w - 3],\ [491, 491, w^2 - 8*w - 4],\ [499, 499, -6*w^2 + 14*w + 31],\ [509, 509, -w - 8],\ [523, 523, 2*w^2 + 1],\ [529, 23, 2*w^2 - 5*w - 22],\ [541, 541, -w^2 + 5*w - 7],\ [547, 547, 2*w^2 - 6*w - 13],\ [563, 563, 2*w^2 - 9*w - 4],\ [569, 569, 4*w^2 - 7*w - 26],\ [569, 569, -3*w^2 + 5*w + 3],\ [569, 569, 4*w^2 - 6*w - 27],\ [577, 577, 3*w^2 - 7*w - 21],\ [577, 577, -8*w^2 + 12*w + 69],\ [577, 577, -2*w^2 + w + 26],\ [587, 587, w^2 - 6*w - 8],\ [593, 593, -2*w^2 + w + 16],\ [593, 593, 3*w^2 - 5*w - 17],\ [593, 593, 2*w^2 - 8*w - 9],\ [601, 601, -6*w^2 + 8*w + 53],\ [607, 607, -2*w - 9],\ [613, 613, w^2 + 2*w - 6],\ [617, 617, 5*w^2 - 11*w - 31],\ [619, 619, -4*w^2 + 6*w + 37],\ [641, 641, 3*w^2 - 6*w - 14],\ [647, 647, -2*w^2 + 3*w + 22],\ [653, 653, 2*w^2 - 7*w - 22],\ [653, 653, 2*w^2 + w + 2],\ [653, 653, -3*w^2 + 5*w + 29],\ [659, 659, 4*w^2 - 11*w - 18],\ [659, 659, 3*w^2 - 6*w - 8],\ [659, 659, 4*w^2 - 8*w - 23],\ [661, 661, w^2 + w - 11],\ [677, 677, -w^2 - 4],\ [701, 701, -2*w^2 - 5*w + 2],\ [727, 727, -2*w^2 + w + 18],\ [733, 733, -9*w^2 + 13*w + 79],\ [733, 733, -7*w^2 + 10*w + 56],\ [733, 733, 2*w^2 - 13],\ [739, 739, 6*w^2 - 10*w - 43],\ [739, 739, 4*w^2 - 4*w - 29],\ [739, 739, -8*w^2 + 15*w + 58],\ [751, 751, -11*w^2 + 19*w + 87],\ [757, 757, 3*w^2 - 10*w - 12],\ [761, 761, 4*w - 3],\ [769, 769, 3*w^2 - w - 13],\ [811, 811, 5*w^2 - 9*w - 33],\ [823, 823, 2*w^2 - 7*w - 12],\ [853, 853, -7*w - 8],\ [853, 853, -3*w^2 + 4*w + 2],\ [853, 853, 2*w^2 + 5*w + 6],\ [857, 857, 10*w^2 - 15*w - 82],\ [857, 857, 3*w^2 - 8*w - 18],\ [857, 857, -4*w^2 + 3*w + 44],\ [859, 859, -w^2 + 4*w - 6],\ [877, 877, -4*w^2 + 13*w + 14],\ [881, 881, 2*w^2 - 9*w - 2],\ [887, 887, 3*w - 14],\ [907, 907, -11*w^2 + 21*w + 77],\ [919, 919, 12*w^2 - 21*w - 92],\ [929, 929, w^2 - 18],\ [937, 937, 9*w + 4],\ [941, 941, -2*w^2 + 2*w - 1],\ [947, 947, 4*w^2 - 9*w - 18],\ [953, 953, -7*w^2 + 14*w + 48],\ [977, 977, w^2 - 2*w - 16],\ [983, 983, 4*w^2 - 7*w - 24],\ [991, 991, -3*w^2 - 2*w + 4]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -4, 0, -2, 2, 4, 2, 8, 2, 8, -6, -4, 6, -4, -6, 6, 10, 16, 12, 12, -10, 6, 2, 14, 4, -4, 0, 4, -14, -20, 14, 20, -24, -22, 20, -20, 24, -22, -2, 24, 4, -8, 6, 22, -22, 14, -14, 12, -20, 20, -12, 4, -6, 22, -4, 6, -6, -24, -28, 24, -20, 34, -26, -4, 12, 0, -24, -20, 2, -32, -22, -30, -8, 6, 10, -16, -18, -12, 22, -4, 2, 18, 38, 18, -18, -2, 8, 24, 8, 0, 14, 12, 0, 8, 12, -12, 32, 26, -10, 10, -18, 4, -26, -26, 20, -36, -18, -22, -24, 14, 30, 18, 40, -16, -14, -14, -20, 16, 34, -26, -4, 8, 28, -2, 18, 26, 24, 34, 10, 12, 30, -22, 14, 34, -36, -46, 6, -26, -8, 0, 22, -6, -14, 46, 28, -46, -22, -10, 12, -26, 42, 44, -18, 0, -48, 12, 16, -42, -22, 6, 46, -6, -2, -4, 16] 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 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]