/* 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([2, 1, -5, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([4, 2, -w^3 + w^2 + 4*w - 2]) primes_array = [ [2, 2, w],\ [2, 2, w + 1],\ [7, 7, w^3 - w^2 - 4*w + 1],\ [17, 17, -w^2 + w + 3],\ [19, 19, -2*w + 1],\ [29, 29, -w^3 + w^2 + 2*w - 1],\ [31, 31, -w^3 + 2*w^2 + 3*w - 5],\ [37, 37, -w^3 + 2*w^2 + 5*w - 5],\ [43, 43, -2*w^3 + 2*w^2 + 8*w + 3],\ [43, 43, -w^2 + 3*w + 1],\ [47, 47, -w^3 + 2*w^2 + 3*w - 1],\ [53, 53, -w^3 + w^2 + 6*w + 1],\ [59, 59, 2*w^3 - 2*w^2 - 10*w + 3],\ [61, 61, w^3 - w^2 - 6*w + 3],\ [61, 61, w^2 + w - 3],\ [71, 71, -w^3 + 5*w + 1],\ [71, 71, w^3 - w^2 - 4*w - 3],\ [81, 3, -3],\ [83, 83, -3*w^3 + 5*w^2 + 12*w - 9],\ [83, 83, -3*w^3 + 6*w^2 + 13*w - 13],\ [89, 89, w^2 - 3*w - 3],\ [97, 97, 2*w - 3],\ [103, 103, -w^3 + w^2 + 2*w - 3],\ [107, 107, 2*w^3 - 2*w^2 - 8*w + 5],\ [107, 107, -2*w^3 + 3*w^2 + 9*w - 9],\ [109, 109, -3*w^3 + 4*w^2 + 13*w - 9],\ [137, 137, -w^3 + w^2 + 6*w - 1],\ [137, 137, 3*w^3 - 3*w^2 - 12*w - 5],\ [139, 139, 2*w^3 - w^2 - 11*w - 3],\ [149, 149, w^3 + w^2 - 6*w - 3],\ [149, 149, -3*w^3 + 5*w^2 + 12*w - 13],\ [149, 149, 2*w^3 - 2*w^2 - 8*w + 1],\ [149, 149, -w^3 + 2*w^2 + w - 3],\ [157, 157, w^3 - 2*w^2 - 5*w + 1],\ [163, 163, w^3 + w^2 - 8*w - 3],\ [163, 163, -w^3 - w^2 + 6*w + 5],\ [169, 13, -w^3 + 2*w^2 + 5*w - 7],\ [169, 13, w^3 - 3*w - 3],\ [173, 173, w^3 - 3*w^2 - 2*w + 9],\ [173, 173, -2*w^2 + 4*w + 1],\ [181, 181, -2*w^3 - w^2 + 13*w + 7],\ [181, 181, 2*w^2 - 2*w - 7],\ [181, 181, 2*w^2 - 4*w - 5],\ [181, 181, 4*w^3 - 5*w^2 - 19*w + 11],\ [191, 191, -3*w^3 + 6*w^2 + 9*w - 11],\ [193, 193, 2*w^3 - 2*w^2 - 10*w + 5],\ [193, 193, -3*w^3 + 2*w^2 + 13*w + 5],\ [199, 199, 2*w^2 - 5],\ [211, 211, -w^3 + 3*w^2 + 2*w - 5],\ [211, 211, w^3 - 2*w^2 + w - 1],\ [223, 223, -w^3 + 5*w - 1],\ [223, 223, -w^3 + 3*w^2 + 4*w - 3],\ [227, 227, w^3 + 2*w^2 - 9*w - 7],\ [241, 241, 2*w^3 - 3*w^2 - 9*w + 3],\ [241, 241, -w^2 + w + 7],\ [263, 263, w^3 - w^2 - 4*w + 5],\ [277, 277, 7*w^3 - 12*w^2 - 27*w + 25],\ [283, 283, w^3 - w^2 - 2*w - 3],\ [311, 311, 2*w^3 - 4*w^2 - 6*w + 9],\ [311, 311, -w^3 + 4*w^2 - w - 5],\ [317, 317, 3*w^3 - 5*w^2 - 10*w + 5],\ [331, 331, w^3 + w^2 - 8*w - 7],\ [337, 337, 2*w^3 - 2*w^2 - 10*w - 3],\ [337, 337, w^3 - 6*w^2 + 7*w + 7],\ [337, 337, -4*w^3 + 5*w^2 + 17*w - 5],\ [337, 337, -3*w^3 + 7*w^2 + 8*w - 15],\ [343, 7, 5*w^3 - 4*w^2 - 23*w - 1],\ [347, 347, -2*w^3 - w^2 + 11*w + 13],\ [349, 349, 4*w^3 - 2*w^2 - 20*w - 5],\ [359, 359, -w^3 + 3*w^2 - 5],\ [367, 367, -2*w^3 + w^2 + 13*w - 5],\ [373, 373, -5*w^3 + 7*w^2 + 20*w - 13],\ [379, 379, -2*w^3 + 3*w^2 + 7*w + 1],\ [379, 379, -5*w^3 + 6*w^2 + 23*w - 11],\ [383, 383, 5*w^3 - 7*w^2 - 22*w + 13],\ [383, 383, 3*w^3 - 5*w^2 - 14*w + 9],\ [397, 397, w^2 - 3*w - 5],\ [397, 397, -w^3 + 2*w^2 + 7*w - 1],\ [401, 401, -w^3 + 3*w^2 + 6*w - 7],\ [401, 401, 2*w^3 - 5*w^2 - w - 1],\ [419, 419, -w^3 + w^2 + 8*w - 5],\ [439, 439, -3*w^3 + 3*w^2 + 12*w + 1],\ [479, 479, 2*w^3 - 8*w^2 + 4*w + 7],\ [491, 491, 2*w^3 - 5*w^2 - 7*w + 13],\ [499, 499, -4*w^3 + 7*w^2 + 17*w - 17],\ [503, 503, 2*w^3 - 4*w^2 - 6*w + 3],\ [509, 509, 2*w^3 - w^2 - 11*w + 1],\ [521, 521, w^3 - 4*w^2 - w + 11],\ [529, 23, 5*w^3 - 7*w^2 - 20*w + 11],\ [529, 23, -w^3 + 5*w^2 - 17],\ [547, 547, 2*w^3 - w^2 - 9*w + 1],\ [547, 547, w^3 - 3*w^2 - 4*w + 1],\ [557, 557, 2*w^3 - 4*w^2 - 8*w + 5],\ [557, 557, 2*w^3 - 5*w^2 - 5*w + 7],\ [563, 563, -4*w^3 + 5*w^2 + 19*w - 13],\ [563, 563, -5*w^3 + 3*w^2 + 24*w + 11],\ [571, 571, -w^3 + 4*w^2 - 3*w - 5],\ [577, 577, w^3 + 2*w^2 - 7*w - 11],\ [587, 587, 2*w^3 - 2*w^2 - 6*w + 1],\ [593, 593, -w^3 + 2*w^2 + w - 5],\ [599, 599, -2*w^3 + 4*w^2 + 6*w - 11],\ [601, 601, 3*w^3 - 4*w^2 - 11*w + 5],\ [601, 601, 2*w^3 - 2*w^2 - 6*w - 5],\ [613, 613, -2*w^3 + 12*w + 3],\ [613, 613, 5*w^3 - 6*w^2 - 23*w + 7],\ [613, 613, 3*w^3 - 3*w^2 - 16*w + 9],\ [613, 613, w^2 + w - 7],\ [617, 617, 3*w^3 - 5*w^2 - 6*w - 3],\ [619, 619, 3*w^3 - 3*w^2 - 16*w + 7],\ [625, 5, -5],\ [641, 641, 3*w^3 - 4*w^2 - 9*w + 13],\ [641, 641, -w^2 + w - 3],\ [647, 647, -w^2 - w - 3],\ [653, 653, 5*w^3 - 5*w^2 - 22*w + 3],\ [661, 661, -4*w^3 + 5*w^2 + 17*w - 11],\ [661, 661, w^3 - 2*w^2 - 7*w + 3],\ [677, 677, w^3 - 3*w - 5],\ [683, 683, 5*w^3 - w^2 - 28*w - 13],\ [701, 701, -2*w^3 + 5*w^2 + 5*w - 9],\ [709, 709, 2*w^3 - w^2 - 7*w - 5],\ [727, 727, -w^3 + 4*w^2 + w - 15],\ [727, 727, 5*w^3 - 6*w^2 - 21*w + 7],\ [733, 733, -w^3 - w^2 + 6*w + 1],\ [733, 733, 4*w^3 - 4*w^2 - 18*w + 5],\ [743, 743, w^3 + w^2 - 4*w - 7],\ [751, 751, 3*w^3 - 3*w^2 - 12*w + 1],\ [751, 751, -2*w^3 + 3*w^2 + 11*w - 11],\ [757, 757, 7*w^3 - 7*w^2 - 32*w + 3],\ [769, 769, 2*w^3 - 6*w^2 - 2*w + 11],\ [769, 769, w^3 - 2*w^2 - 3*w - 3],\ [773, 773, -2*w^3 + 3*w^2 + 9*w - 1],\ [797, 797, 3*w^3 - 5*w^2 - 8*w + 3],\ [797, 797, -4*w^3 + 2*w^2 + 18*w + 7],\ [809, 809, 2*w^2 - 4*w - 7],\ [809, 809, w^3 - 2*w^2 - w + 9],\ [823, 823, 2*w^3 - 5*w^2 - 9*w + 7],\ [823, 823, -w^3 + 5*w^2 + 2*w - 21],\ [853, 853, 4*w^3 - 7*w^2 - 15*w + 11],\ [857, 857, -w^3 + 4*w^2 + 3*w - 15],\ [877, 877, 6*w^3 - 3*w^2 - 27*w - 13],\ [881, 881, 2*w^2 - 9],\ [881, 881, -2*w^3 + 3*w^2 + 11*w - 3],\ [881, 881, 3*w^3 - 2*w^2 - 13*w - 9],\ [881, 881, -5*w^2 + 5*w + 21],\ [907, 907, -w^3 + 5*w^2 + 2*w - 19],\ [907, 907, -6*w^3 + 9*w^2 + 23*w - 17],\ [911, 911, -4*w^3 + 8*w^2 + 12*w - 15],\ [919, 919, 2*w^3 - 4*w^2 - 6*w + 1],\ [937, 937, 2*w^2 - 13],\ [941, 941, -3*w^3 + 17*w + 7],\ [947, 947, -2*w^3 + 14*w - 1],\ [947, 947, -4*w^3 + 6*w^2 + 14*w - 15],\ [953, 953, 2*w^3 + w^2 - 15*w - 7],\ [953, 953, -3*w^3 + 5*w^2 + 8*w - 5],\ [977, 977, -4*w^3 + 4*w^2 + 22*w - 13]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -1, 3, 7, 2, -8, 1, -5, 11, 11, -7, 1, 6, -7, 4, -5, -16, 5, -4, 4, -2, -10, 17, 9, -2, 11, -17, -16, -8, -15, 18, -18, 4, -7, 21, -1, 6, 17, 13, -24, -5, -5, 16, 16, 17, -4, -18, 24, -8, -25, -18, -7, 8, 22, 22, 0, 14, 13, 7, 26, -12, -35, -14, -30, 19, -8, 8, 26, 20, 14, -28, 0, -16, 17, 12, 12, 20, -2, 5, -16, -2, -11, -4, -36, 28, 9, -7, -6, -2, 20, 20, 9, -36, -14, 25, -19, -11, -38, -16, -44, 5, -8, 36, -2, 2, -2, -20, 42, -4, -23, -48, -18, 10, -5, -42, 20, -29, 31, -2, -6, -13, -46, -14, 19, 4, -26, -48, -34, 44, 0, 15, -6, 5, 15, 48, -56, 34, -26, 44, 46, -35, -24, 2, -42, -6, 16, 12, -15, -25, 29, 24, 20, -30, -8, -12] 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 AL_eigenvalues[ZF.ideal([2, 2, w + 1])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]