/* 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, -3, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([31, 31, w^3 - 6*w - 1]) primes_array = [ [7, 7, w - 1],\ [9, 3, w^3 - 5*w - 2],\ [9, 3, w^3 - w^2 - 4*w],\ [13, 13, -w + 2],\ [16, 2, 2],\ [17, 17, w^3 - w^2 - 5*w],\ [19, 19, -w^3 + w^2 + 6*w],\ [23, 23, -w^2 + w + 3],\ [29, 29, w^3 - 5*w],\ [31, 31, w^3 - 6*w - 1],\ [31, 31, w^2 - 2],\ [37, 37, -w - 3],\ [37, 37, w^3 - 4*w - 1],\ [37, 37, w^3 - 7*w - 4],\ [37, 37, w^2 - 3],\ [43, 43, w^2 + w - 3],\ [43, 43, w^3 - w^2 - 5*w - 1],\ [47, 47, -w^3 + w^2 + 5*w - 4],\ [53, 53, w^3 - 6*w],\ [61, 61, w^3 - w^2 - 7*w - 2],\ [67, 67, -w^3 + 4*w - 2],\ [73, 73, w^3 - 7*w - 3],\ [79, 79, w^3 - 7*w - 2],\ [79, 79, -2*w^3 + w^2 + 10*w],\ [83, 83, -2*w^3 + 11*w + 4],\ [101, 101, -2*w^3 + w^2 + 10*w + 2],\ [101, 101, w^3 - w^2 - 6*w - 2],\ [109, 109, -3*w - 1],\ [113, 113, 2*w^3 - w^2 - 10*w - 1],\ [149, 149, w^2 - 2*w - 8],\ [157, 157, w^3 + w^2 - 5*w - 7],\ [163, 163, 3*w^3 - 2*w^2 - 15*w - 1],\ [167, 167, 3*w^3 - w^2 - 16*w - 3],\ [173, 173, -w - 4],\ [173, 173, w^2 - 2*w - 5],\ [179, 179, -w^3 + 2*w^2 + 4*w - 4],\ [181, 181, -w^3 + 2*w^2 + 6*w - 6],\ [191, 191, 2*w^2 - 3*w - 7],\ [191, 191, 2*w^2 - w - 3],\ [197, 197, 2*w^3 - w^2 - 13*w - 4],\ [197, 197, w^3 + w^2 - 8*w - 3],\ [223, 223, 3*w^3 - w^2 - 16*w - 4],\ [227, 227, -w^3 + 2*w^2 + 5*w - 5],\ [227, 227, w^3 - 4*w - 5],\ [239, 239, 2*w^3 - 11*w - 3],\ [239, 239, -2*w^3 + 2*w^2 + 10*w - 7],\ [239, 239, w^3 - w^2 - 5*w - 4],\ [239, 239, w^3 - 4*w - 7],\ [257, 257, -2*w^3 + w^2 + 9*w],\ [263, 263, -w^3 + 2*w^2 + 5*w - 4],\ [269, 269, 2*w^3 - w^2 - 9*w - 3],\ [269, 269, w^3 - w^2 - 4*w - 4],\ [281, 281, 3*w - 2],\ [281, 281, 4*w^3 - 2*w^2 - 21*w],\ [293, 293, w^3 - 4*w - 6],\ [307, 307, 2*w^3 - 13*w - 6],\ [307, 307, -w^3 + 3*w^2 + 3*w - 11],\ [311, 311, 3*w^3 - w^2 - 18*w - 7],\ [311, 311, w^2 + w - 5],\ [313, 313, -w^3 + w^2 + 7*w - 4],\ [313, 313, w^2 - w - 8],\ [337, 337, -2*w^3 + w^2 + 9*w + 2],\ [343, 7, w^3 + w^2 - 5*w - 8],\ [347, 347, 2*w^3 - 3*w^2 - 11*w + 2],\ [347, 347, w^3 - w^2 - 2*w - 3],\ [353, 353, 3*w^3 - 2*w^2 - 15*w - 3],\ [353, 353, w^3 - 6*w - 7],\ [359, 359, -2*w^3 + w^2 + 12*w + 5],\ [367, 367, 2*w^3 - 2*w^2 - 13*w + 4],\ [373, 373, -3*w^3 + w^2 + 15*w + 7],\ [373, 373, w^3 + w^2 - 8*w - 11],\ [389, 389, 3*w^3 - w^2 - 17*w - 1],\ [397, 397, -3*w^3 + w^2 + 16*w + 9],\ [397, 397, 2*w^2 - w - 4],\ [401, 401, -w^3 + w^2 + 3*w - 4],\ [421, 421, 3*w^3 - 2*w^2 - 14*w - 6],\ [421, 421, 2*w^2 + w - 4],\ [433, 433, 2*w^3 - w^2 - 13*w - 3],\ [433, 433, 2*w^3 - w^2 - 12*w - 6],\ [439, 439, 2*w^3 - w^2 - 13*w - 7],\ [439, 439, w^3 - 3*w - 4],\ [457, 457, 2*w^2 - 7],\ [457, 457, 2*w^3 - 2*w^2 - 10*w - 5],\ [461, 461, w - 5],\ [463, 463, w^3 + 2*w^2 - 5*w - 9],\ [463, 463, w^3 + w^2 - 8*w - 10],\ [467, 467, -4*w^3 + 2*w^2 + 21*w + 3],\ [467, 467, w^3 + 2*w^2 - 8*w - 6],\ [491, 491, -w - 5],\ [491, 491, 3*w^3 - w^2 - 17*w - 7],\ [499, 499, w^3 - 2*w^2 - 7*w + 5],\ [503, 503, -2*w^3 + 3*w^2 + 8*w],\ [541, 541, 2*w^3 - w^2 - 13*w],\ [541, 541, -3*w^3 + 3*w^2 + 17*w - 2],\ [557, 557, -2*w^3 + w^2 + 8*w + 1],\ [563, 563, -4*w^3 + 3*w^2 + 22*w - 1],\ [563, 563, 3*w^3 - 2*w^2 - 16*w - 2],\ [571, 571, 2*w^2 - w - 7],\ [571, 571, 3*w^3 - 2*w^2 - 18*w + 1],\ [593, 593, w^3 + 2*w^2 - 7*w - 8],\ [601, 601, 2*w^2 - 5],\ [613, 613, 3*w^3 - w^2 - 15*w - 2],\ [613, 613, -w^3 + 3*w^2 + 3*w - 3],\ [617, 617, 3*w^3 - 19*w - 10],\ [617, 617, 2*w^3 - w^2 - 13*w - 1],\ [625, 5, -5],\ [631, 631, 3*w^3 - w^2 - 17*w],\ [631, 631, w^3 + w^2 - 5*w - 10],\ [643, 643, -3*w^3 + 2*w^2 + 14*w - 1],\ [647, 647, -2*w^3 + 13*w],\ [653, 653, -3*w^3 + 2*w^2 + 17*w + 2],\ [661, 661, -3*w^3 + w^2 + 13*w + 9],\ [661, 661, -2*w^3 + 2*w^2 + 13*w + 2],\ [673, 673, -4*w^3 + w^2 + 22*w + 4],\ [677, 677, 2*w^3 - 3*w^2 - 8*w - 2],\ [677, 677, 3*w^3 - w^2 - 18*w - 8],\ [683, 683, -w^3 + 2*w^2 + 6*w - 8],\ [683, 683, -w^3 - 2*w^2 + 5*w + 8],\ [709, 709, 3*w^3 - w^2 - 19*w - 7],\ [709, 709, 2*w^3 - 12*w - 1],\ [719, 719, w^3 - w^2 - 4*w - 5],\ [719, 719, 2*w^2 - 4*w - 7],\ [733, 733, -2*w^3 + 3*w^2 + 10*w - 6],\ [743, 743, 2*w^3 - 2*w^2 - 14*w - 1],\ [743, 743, 2*w^3 - 11*w],\ [757, 757, -w^3 + 2*w^2 + w - 4],\ [769, 769, w^3 + w^2 - 4*w - 7],\ [769, 769, -w^3 + 2*w^2 + 2*w - 5],\ [787, 787, 3*w^3 - w^2 - 15*w - 5],\ [797, 797, -4*w^3 + 3*w^2 + 19*w - 6],\ [797, 797, -3*w^3 + 2*w^2 + 14*w],\ [811, 811, -w^2 - 3],\ [811, 811, -w^3 + w^2 + 8*w - 4],\ [821, 821, 2*w^3 - 2*w^2 - 10*w - 3],\ [821, 821, -3*w^3 + w^2 + 12*w + 8],\ [823, 823, -w^3 + w^2 + 2*w - 4],\ [829, 829, w^3 - 7*w + 4],\ [829, 829, 3*w^3 - 19*w - 4],\ [839, 839, w^2 - w - 9],\ [853, 853, 3*w^3 - w^2 - 15*w - 4],\ [863, 863, w^3 + w^2 - 8*w - 13],\ [863, 863, w^2 - 3*w - 7],\ [863, 863, -w^3 + w^2 + 4*w - 7],\ [863, 863, -w^2 + w - 3],\ [877, 877, -2*w^3 + 3*w^2 + 6*w - 4],\ [919, 919, 2*w^3 - 14*w - 7],\ [929, 929, 2*w^3 + w^2 - 13*w - 6],\ [937, 937, -w^3 + 3*w^2 + 7*w - 4],\ [937, 937, -3*w^3 + 4*w^2 + 16*w - 5],\ [941, 941, -4*w^3 + w^2 + 24*w + 11],\ [941, 941, w^2 + 2*w - 5],\ [947, 947, w^3 - 9*w - 1],\ [953, 953, 4*w^3 - w^2 - 21*w - 9],\ [961, 31, 3*w^3 - 2*w^2 - 16*w - 3],\ [967, 967, 4*w^3 - 21*w - 9],\ [971, 971, 3*w^3 - w^2 - 18*w - 9],\ [971, 971, -w^3 + 2*w^2 + 3*w - 8]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-2, -2, -4, 2, 1, -2, -4, -6, -2, 1, -4, -6, 4, 10, 8, -2, 8, 8, 0, 6, 0, 10, 0, -4, -6, 6, -18, 10, -12, -10, -10, 10, 16, -6, 18, -4, 20, 16, -14, 10, 26, 6, -4, 10, 10, -24, -20, -26, 10, -20, -28, 6, 28, 0, -2, -4, -12, 32, -6, -22, -10, -8, -12, 12, 6, 30, 14, -16, 12, 2, 22, -16, -14, -2, -2, -22, -8, 14, 2, 0, 18, -34, -18, -38, 32, 40, -8, 18, 24, 32, 12, 24, -10, 6, -22, -20, -24, -30, 12, 20, -20, -22, -34, -38, 38, 34, 20, 30, -46, -28, 18, -10, -18, -12, 26, 6, -2, -18, 18, -10, -24, -8, 48, -24, -22, -10, 40, 2, 2, 30, -12, 0, -40, -6, 16, -8, -34, 28, -16, -32, -8, 56, -24, -12, 54, -40, -50, 54, -22, 10, -60, 24, -18, -30, 34, -36, -52] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([31, 31, w^3 - 6*w - 1])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]