/* 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([1, 4, -3, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([33, 33, 2*w - 1]) primes_array = [ [3, 3, -w - 1],\ [4, 2, -w^3 + w^2 + 3*w],\ [11, 11, -w^2 + 3],\ [13, 13, w^3 - 2*w^2 - w + 1],\ [13, 13, w^3 - w^2 - 2*w + 1],\ [23, 23, -w^3 + w^2 + 4*w - 2],\ [23, 23, w^3 - 2*w^2 - 3*w + 2],\ [47, 47, -w^3 + 2*w^2 + 3*w - 1],\ [47, 47, -w^3 + w^2 + 4*w - 3],\ [59, 59, w^2 - 5],\ [59, 59, w^2 - 2*w - 4],\ [61, 61, -w^3 + 2*w^2 + 4*w - 4],\ [61, 61, w^3 - w^2 - 5*w + 1],\ [71, 71, w^3 - w^2 - 2*w - 2],\ [71, 71, -w^3 + 2*w^2 + w - 4],\ [73, 73, 2*w^2 - w - 5],\ [73, 73, w^3 - 2*w^2 - 2*w + 6],\ [83, 83, -2*w^3 + 3*w^2 + 6*w - 6],\ [83, 83, -2*w^3 + 4*w^2 + 5*w - 5],\ [83, 83, -2*w^3 + 2*w^2 + 7*w - 2],\ [83, 83, 2*w^3 - 3*w^2 - 6*w + 1],\ [97, 97, -w - 3],\ [97, 97, 2*w^2 - 3*w - 3],\ [97, 97, 2*w^2 - w - 4],\ [97, 97, w - 4],\ [107, 107, -w^3 + 3*w^2 - 5],\ [107, 107, -2*w^3 + w^2 + 6*w - 1],\ [107, 107, 2*w^3 - 5*w^2 - 2*w + 4],\ [107, 107, w^3 - 3*w - 3],\ [109, 109, 2*w^3 - 3*w^2 - 5*w + 4],\ [109, 109, -2*w^3 + 3*w^2 + 5*w - 2],\ [121, 11, 2*w^2 - 2*w - 3],\ [157, 157, 2*w^3 - 2*w^2 - 9*w + 3],\ [157, 157, -w^3 + 2*w^2 + 3*w - 7],\ [157, 157, -w^3 + w^2 + 4*w + 3],\ [157, 157, -2*w^3 + 4*w^2 + 7*w - 6],\ [169, 13, 2*w^3 - 2*w^2 - 9*w],\ [179, 179, w^3 + 2],\ [179, 179, -2*w^3 + w^2 + 10*w - 1],\ [191, 191, -2*w^3 + 5*w^2 + 4*w - 7],\ [191, 191, 2*w^3 - w^2 - 8*w],\ [193, 193, 3*w^2 - 2*w - 9],\ [193, 193, 3*w^2 - 4*w - 8],\ [227, 227, -w^3 + 3*w^2 + 3*w - 3],\ [227, 227, w^3 - 3*w - 4],\ [227, 227, -w^3 + 3*w^2 - 6],\ [227, 227, w^3 - 6*w + 2],\ [229, 229, w^3 + w^2 - 6*w - 4],\ [229, 229, w^3 + w^2 - 5*w - 3],\ [229, 229, 2*w^3 - 9*w - 3],\ [229, 229, -w^3 + 4*w^2 + w - 8],\ [241, 241, 2*w^3 - 3*w^2 - 4*w + 2],\ [241, 241, -2*w^3 + 3*w^2 + 4*w - 3],\ [251, 251, -2*w^3 + 4*w^2 + 4*w - 1],\ [251, 251, -2*w^3 + 2*w^2 + 6*w - 5],\ [277, 277, w^3 - w^2 - 6*w + 1],\ [277, 277, -w^3 + 2*w^2 + 5*w - 5],\ [289, 17, w^3 - w^2 - 6*w + 3],\ [289, 17, -w^3 + 2*w^2 + 5*w - 3],\ [311, 311, 2*w^3 - 3*w^2 - 3*w + 6],\ [311, 311, -3*w^3 + 7*w^2 + 8*w - 12],\ [337, 337, -w^3 + w^2 + 4*w - 6],\ [337, 337, -2*w^3 + 3*w^2 + 8*w - 5],\ [347, 347, 2*w^3 - 6*w^2 - 5*w + 10],\ [347, 347, 4*w^3 - 5*w^2 - 13*w + 6],\ [347, 347, -4*w^3 + 7*w^2 + 11*w - 8],\ [347, 347, -2*w^3 + 11*w + 1],\ [349, 349, 3*w^2 - w - 6],\ [349, 349, -2*w^3 + 3*w^2 + 10*w + 3],\ [359, 359, 2*w^3 - 2*w^2 - 7*w + 4],\ [359, 359, -3*w^3 + 4*w^2 + 11*w - 7],\ [359, 359, w^3 - 2*w^2 + w - 4],\ [359, 359, 2*w^3 - 4*w^2 - 5*w + 3],\ [373, 373, -3*w^3 + 3*w^2 + 9*w - 1],\ [373, 373, w^3 + 2*w^2 - 7*w - 9],\ [383, 383, 2*w^2 - 7],\ [383, 383, 2*w^2 - 4*w - 5],\ [409, 409, -w^3 + 5*w^2 - 3*w - 7],\ [409, 409, -w^3 - 2*w^2 + 4*w + 6],\ [419, 419, w^3 - 3*w - 6],\ [419, 419, -w^3 + 3*w^2 - 8],\ [443, 443, -3*w^3 + 5*w^2 + 10*w - 12],\ [443, 443, -3*w^3 + 7*w^2 + 7*w - 11],\ [457, 457, -w^3 + 2*w^2 + 3*w - 8],\ [457, 457, w^3 - w^2 - 4*w - 4],\ [467, 467, w^2 + 2*w - 6],\ [467, 467, w^2 - 4*w - 3],\ [491, 491, 3*w^3 - 2*w^2 - 10*w - 4],\ [491, 491, -2*w^3 + 2*w^2 + 7*w - 5],\ [491, 491, -2*w^3 + 4*w^2 + 5*w - 2],\ [491, 491, -3*w^3 + 7*w^2 + 5*w - 13],\ [529, 23, 3*w^2 - 3*w - 4],\ [541, 541, 2*w^3 - 2*w^2 - 5*w + 7],\ [541, 541, -4*w^3 + 7*w^2 + 10*w - 12],\ [577, 577, 3*w^2 - 2*w - 7],\ [577, 577, -3*w^3 + 6*w^2 + 10*w - 10],\ [577, 577, -2*w^3 - w^2 + 7*w + 4],\ [577, 577, 3*w^2 - 4*w - 6],\ [587, 587, 2*w^3 - w^2 - 6*w - 4],\ [587, 587, 2*w^3 - w^2 - 11*w - 4],\ [599, 599, -4*w^3 + 3*w^2 + 14*w + 5],\ [599, 599, -w^3 + 7*w + 5],\ [601, 601, 3*w^3 - 4*w^2 - 8*w + 4],\ [601, 601, -3*w^3 + 5*w^2 + 7*w - 5],\ [613, 613, 3*w^2 - 2*w - 6],\ [613, 613, 3*w^2 - 4*w - 5],\ [625, 5, -5],\ [647, 647, 3*w^3 - 3*w^2 - 12*w + 4],\ [647, 647, -3*w^3 + 6*w^2 + 9*w - 8],\ [661, 661, w^3 + 2*w^2 - 5*w - 7],\ [661, 661, -w^2 - 3],\ [661, 661, -w^2 + 2*w - 4],\ [661, 661, -w^3 + 5*w^2 - 2*w - 9],\ [673, 673, 3*w^3 - 3*w^2 - 8*w + 2],\ [673, 673, -3*w^3 + 6*w^2 + 5*w - 6],\ [683, 683, -w^3 + 3*w^2 - 2*w - 4],\ [683, 683, w^3 - w - 4],\ [709, 709, 4*w^3 - 7*w^2 - 10*w + 8],\ [709, 709, w^3 - w^2 - 3*w - 5],\ [709, 709, -w^3 + 2*w^2 + 2*w - 8],\ [709, 709, -w^3 + 5*w^2 + w - 9],\ [719, 719, 2*w^3 - w^2 - 8*w + 2],\ [719, 719, -2*w^3 + 5*w^2 + 4*w - 5],\ [733, 733, -w^3 + 5*w^2 - w - 11],\ [733, 733, 3*w^3 - 5*w^2 - 6*w + 7],\ [743, 743, w^2 - 4*w - 4],\ [743, 743, -3*w^3 + 7*w^2 + 6*w - 9],\ [743, 743, 3*w^3 - 2*w^2 - 11*w + 1],\ [743, 743, w^2 + 2*w - 7],\ [769, 769, -2*w^2 - 3*w + 4],\ [769, 769, 4*w^3 - 4*w^2 - 14*w - 5],\ [827, 827, -w^2 + 4*w + 7],\ [827, 827, -2*w^3 + w^2 + 7*w - 4],\ [827, 827, -2*w^3 + 5*w^2 + 3*w - 2],\ [827, 827, -2*w^3 + w^2 + 11*w + 6],\ [829, 829, -2*w^3 + 4*w^2 + 8*w - 9],\ [829, 829, -3*w^3 + 5*w^2 + 6*w - 3],\ [829, 829, 3*w^3 - 4*w^2 - 7*w + 5],\ [829, 829, 2*w^3 - 2*w^2 - 10*w + 1],\ [839, 839, 2*w^3 - 9*w],\ [839, 839, 2*w^2 - 4*w - 7],\ [841, 29, -4*w^3 + 9*w^2 + 6*w - 11],\ [841, 29, 4*w^2 - 3*w - 12],\ [853, 853, -3*w^3 + 5*w^2 + 11*w - 7],\ [853, 853, -3*w^3 + 4*w^2 + 12*w - 6],\ [863, 863, -3*w^3 + 2*w^2 + 10*w - 2],\ [863, 863, 4*w^3 - 6*w^2 - 11*w + 13],\ [877, 877, -w^3 - w^2 + 10*w],\ [877, 877, w^3 - 3*w^2 - 8*w],\ [887, 887, -3*w^3 + 4*w^2 + 10*w - 8],\ [887, 887, w^3 - 5*w^2 - 4*w + 12],\ [887, 887, w^3 + 2*w^2 - 11*w - 4],\ [887, 887, 3*w^3 - 5*w^2 - 9*w + 3],\ [911, 911, 4*w^3 - 3*w^2 - 14*w + 1],\ [911, 911, 5*w^3 - 6*w^2 - 17*w - 1],\ [937, 937, w^3 + 2*w^2 - 7*w - 7],\ [937, 937, w^3 - 5*w^2 + 11],\ [947, 947, 2*w^3 - w^2 - 10*w + 3],\ [947, 947, -2*w^3 + 5*w^2 + 6*w - 6],\ [961, 31, -4*w^3 + 8*w^2 + 13*w - 13],\ [961, 31, 2*w^3 + w^2 - 8*w - 5],\ [971, 971, -5*w^3 + 7*w^2 + 15*w - 11],\ [971, 971, -2*w^3 + 6*w + 5],\ [983, 983, 2*w^3 - 4*w^2 - 7*w + 1],\ [983, 983, 4*w^2 + 3*w - 3],\ [997, 997, 3*w^3 - 5*w^2 - 6*w + 4],\ [997, 997, -3*w^3 + 4*w^2 + 7*w - 4]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 3, 1, -2, 4, -8, 4, 6, 0, 0, -6, -10, 8, 10, -8, -14, 10, 4, -2, -8, -14, 2, 8, -16, -10, 12, 2, -16, -12, 10, 4, 6, -6, 10, 22, -12, -8, -8, 10, -12, -12, -4, -16, -22, -4, 20, -4, -6, -2, 4, -6, -14, 10, 30, 12, 14, 2, -2, -2, 24, 18, -6, 30, 20, -4, 8, 20, 14, -22, 6, -16, -28, 0, -24, 6, 36, 36, 14, 14, 4, -20, -4, 20, 34, 22, 16, -26, -32, -20, -8, -2, -10, 34, 10, -2, -34, 38, -38, 28, -8, 26, 32, 2, 26, -38, 16, -14, -24, -18, -14, 28, -38, -50, -14, -14, -36, -30, -18, -34, 44, -30, -18, 0, -8, -50, 38, 24, 24, -16, -46, 38, -24, 50, -40, -30, 46, -30, 42, -26, -10, -16, -8, -44, 0, 42, 54, -24, 18, -18, 32, -40, 38, -52, 36, -48, -30, -6, 36, -36, 54, -30, 28, -20, 36, 12, 32, 14] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([3, 3, -w - 1])] = -1 AL_eigenvalues[ZF.ideal([11, 11, -w^2 + 3])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]