/* 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([6, 0, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 2, 2]) primes_array = [ [2, 2, -w^2 + w + 2],\ [3, 3, w^2 - w - 3],\ [11, 11, -w^2 + w + 1],\ [11, 11, -w^2 - w + 1],\ [13, 13, w^3 - 4*w + 1],\ [13, 13, -w^3 + 4*w + 1],\ [25, 5, -w^2 - 2*w + 1],\ [25, 5, w^2 - 2*w - 1],\ [37, 37, w^3 - 3*w - 1],\ [37, 37, w^3 - 3*w + 1],\ [59, 59, w^2 - w - 5],\ [59, 59, -w^2 - w + 5],\ [61, 61, -w^3 + w^2 + 4*w - 7],\ [61, 61, w^3 - 3*w^2 - 6*w + 11],\ [73, 73, 2*w^2 - w - 5],\ [73, 73, 2*w - 1],\ [73, 73, -2*w - 1],\ [73, 73, 2*w^2 + w - 5],\ [83, 83, 2*w^3 + w^2 - 9*w - 7],\ [83, 83, -2*w^3 + w^2 + 7*w + 1],\ [107, 107, w^3 + w^2 - 4*w - 1],\ [107, 107, -w^3 + w^2 + 4*w - 1],\ [109, 109, -w^3 + 2*w^2 + 5*w - 11],\ [109, 109, w^3 + 2*w^2 - 5*w - 11],\ [121, 11, 2*w^2 - 5],\ [131, 131, 3*w^3 - 2*w^2 - 14*w + 11],\ [131, 131, 3*w^3 - 12*w + 5],\ [157, 157, -3*w^3 + 2*w^2 + 13*w - 11],\ [157, 157, -w^3 + 2*w^2 + 7*w - 5],\ [167, 167, w^2 + 2*w - 5],\ [167, 167, -w^3 + w^2 + w + 1],\ [167, 167, 3*w^3 - w^2 - 9*w - 5],\ [167, 167, w^2 - 2*w - 5],\ [169, 13, -w^2 + 7],\ [179, 179, -w^3 + w^2 + 6*w - 1],\ [179, 179, w^3 + w^2 - 6*w - 1],\ [181, 181, -w^3 + 5*w - 5],\ [181, 181, w^3 - 5*w - 5],\ [191, 191, -2*w^3 + 2*w^2 + 6*w - 1],\ [191, 191, -2*w^2 + 2*w + 7],\ [191, 191, -4*w^2 + 4*w + 11],\ [191, 191, -2*w^3 + 8*w + 5],\ [227, 227, -w^3 + 2*w^2 + 5*w - 5],\ [227, 227, w^3 + 2*w^2 - 5*w - 5],\ [229, 229, -w^3 + 3*w + 5],\ [229, 229, -w^3 - 4*w^2 + 7*w + 13],\ [239, 239, -w^3 + w^2 + 5*w - 1],\ [239, 239, 2*w^3 - 4*w^2 - 12*w + 13],\ [239, 239, 2*w^3 - 2*w^2 - 10*w + 7],\ [239, 239, w^3 + w^2 - 5*w - 1],\ [241, 241, 2*w^3 - w^2 - 8*w + 5],\ [241, 241, -3*w^2 + 4*w + 7],\ [241, 241, -2*w^3 + w^2 + 6*w + 1],\ [241, 241, -2*w^3 - w^2 + 8*w + 5],\ [251, 251, -w^3 + 2*w - 5],\ [251, 251, 3*w^3 - 2*w^2 - 12*w + 13],\ [263, 263, 2*w^3 - 2*w^2 - 8*w + 11],\ [263, 263, -w^3 + w^2 + 3*w - 7],\ [263, 263, 3*w^3 - w^2 - 11*w + 11],\ [263, 263, -2*w^3 + 6*w - 7],\ [277, 277, -3*w^2 - w + 11],\ [277, 277, 3*w^2 - w - 11],\ [311, 311, -w^3 + 5*w^2 + 7*w - 19],\ [311, 311, 2*w^3 - 3*w^2 - 8*w + 17],\ [311, 311, -2*w^3 + 6*w - 5],\ [311, 311, -2*w^3 - 2*w^2 + 8*w + 5],\ [337, 337, -2*w^3 + 8*w + 1],\ [337, 337, -w^3 + 3*w^2 + 5*w - 11],\ [337, 337, w^3 + 3*w^2 - 5*w - 11],\ [337, 337, 2*w^3 - 8*w + 1],\ [347, 347, w^3 - 3*w^2 - 6*w + 13],\ [347, 347, -w^3 - 3*w^2 + 6*w + 13],\ [349, 349, -w^3 + 4*w - 5],\ [349, 349, w^3 - 4*w - 5],\ [361, 19, 4*w^3 - 2*w^2 - 17*w + 13],\ [361, 19, 2*w^3 - 2*w^2 - 11*w + 7],\ [373, 373, -2*w^3 - 5*w^2 + 13*w + 17],\ [373, 373, 2*w^3 - w^2 - 7*w + 1],\ [383, 383, 4*w^3 - w^2 - 16*w + 13],\ [383, 383, w^2 + 2*w - 7],\ [383, 383, w^2 - 2*w - 7],\ [383, 383, 2*w^3 + 3*w^2 - 6*w - 5],\ [397, 397, -w^3 + 2*w^2 + 7*w - 7],\ [397, 397, w^3 + 2*w^2 - 7*w - 7],\ [419, 419, 5*w^2 - 5*w - 11],\ [419, 419, 3*w^2 - 3*w - 5],\ [421, 421, w^3 + 4*w^2 - 5*w - 17],\ [421, 421, -w^3 + 4*w^2 + 5*w - 17],\ [433, 433, w^3 - w^2 - 7*w + 1],\ [433, 433, 3*w - 1],\ [433, 433, -3*w - 1],\ [433, 433, 5*w^3 - 3*w^2 - 21*w + 19],\ [443, 443, w^3 - 4*w^2 - 6*w + 17],\ [443, 443, -3*w^3 + 6*w^2 + 16*w - 25],\ [467, 467, -w^3 + w^2 + 2*w - 5],\ [467, 467, w^3 + w^2 - 2*w - 5],\ [491, 491, 3*w^3 - w^2 - 14*w + 7],\ [491, 491, -3*w^3 - w^2 + 14*w + 7],\ [529, 23, 3*w^2 - 11],\ [529, 23, 3*w^2 - 7],\ [541, 541, 3*w^3 + 2*w^2 - 10*w - 1],\ [541, 541, 3*w^3 - 4*w^2 - 16*w + 17],\ [563, 563, w^3 + 2*w^2 - 2*w - 7],\ [563, 563, -w^3 + 2*w^2 + 2*w - 7],\ [587, 587, -2*w^3 + w^2 + 5*w - 5],\ [587, 587, 2*w^3 + w^2 - 5*w - 5],\ [613, 613, 3*w^3 - 13*w - 1],\ [613, 613, 3*w^3 - 13*w + 1],\ [659, 659, w^3 + 3*w^2 - 4*w - 5],\ [659, 659, -w^3 + 3*w^2 + 4*w - 5],\ [661, 661, w^3 + 4*w^2 - 9*w - 13],\ [661, 661, -3*w^3 + 4*w^2 + 7*w - 5],\ [673, 673, -2*w^3 + 7*w + 1],\ [673, 673, w^3 + w^2 - 7*w - 5],\ [673, 673, -w^3 + w^2 + 7*w - 5],\ [673, 673, 2*w^3 - 7*w + 1],\ [683, 683, -2*w^3 - w^2 + 9*w + 1],\ [683, 683, 2*w^3 - w^2 - 9*w + 1],\ [709, 709, -3*w^3 + 2*w^2 + 8*w + 1],\ [709, 709, -w^3 + 4*w^2 - 2*w - 7],\ [733, 733, 2*w^3 - 5*w^2 - 11*w + 19],\ [733, 733, -2*w^3 + w^2 + 7*w - 11],\ [743, 743, 2*w^3 + 2*w^2 - 11*w - 5],\ [743, 743, 2*w^3 - w^2 - 8*w - 1],\ [743, 743, -2*w^3 - w^2 + 8*w - 1],\ [743, 743, -2*w^3 + 2*w^2 + 11*w - 5],\ [757, 757, 2*w^3 + 3*w^2 - 3*w + 1],\ [757, 757, -2*w^3 + 5*w^2 + 11*w - 17],\ [827, 827, -5*w^3 + 4*w^2 + 21*w - 23],\ [827, 827, -w^3 + w - 7],\ [829, 829, 2*w^3 - 3*w^2 - 9*w + 17],\ [829, 829, -2*w^3 - 3*w^2 + 9*w + 17],\ [841, 29, 2*w^2 - w - 13],\ [841, 29, 2*w^2 + w - 13],\ [853, 853, -w^3 + 6*w - 7],\ [853, 853, -2*w^3 + w^2 + 11*w - 5],\ [863, 863, w^3 - 5*w^2 - 9*w + 13],\ [863, 863, 2*w^3 + 4*w^2 - 5*w - 11],\ [863, 863, -2*w^3 + 4*w^2 + 5*w - 11],\ [863, 863, w^3 - 3*w^2 - 7*w + 7],\ [877, 877, -w^3 - 3*w^2 + 4*w + 17],\ [877, 877, w^3 - 3*w^2 - 4*w + 17],\ [887, 887, -2*w^3 - w^2 + 10*w + 1],\ [887, 887, 2*w^3 + 2*w^2 - 9*w - 5],\ [887, 887, -2*w^3 + 2*w^2 + 9*w - 5],\ [887, 887, 2*w^3 - w^2 - 10*w + 1],\ [911, 911, -2*w^3 + 11*w - 5],\ [911, 911, -w^3 + w^2 + w - 5],\ [911, 911, w^3 + w^2 - w - 5],\ [911, 911, 2*w^3 - 11*w - 5],\ [937, 937, -4*w^3 - 2*w^2 + 16*w + 17],\ [937, 937, 3*w^3 - w^2 - 11*w - 1],\ [937, 937, -3*w^3 - 5*w^2 + 17*w + 19],\ [937, 937, -4*w^2 + 2*w + 13],\ [947, 947, -3*w^3 + 2*w^2 + 10*w + 1],\ [947, 947, 3*w^3 - 12*w - 7],\ [971, 971, w^3 + w^2 - 2*w - 7],\ [971, 971, -w^3 + w^2 + 2*w - 7],\ [983, 983, -w^3 - 3*w^2 + 7*w + 13],\ [983, 983, 2*w^3 - 2*w^2 - 7*w + 1],\ [983, 983, -2*w^3 - 2*w^2 + 7*w + 1],\ [983, 983, w^3 - 7*w^2 + 3*w + 17],\ [997, 997, -w^3 + 2*w^2 + 4*w - 13],\ [997, 997, 3*w^3 - 8*w^2 - 18*w + 29]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [0, -2, 0, 4, -4, 4, -6, 2, 6, -10, -6, 2, -6, -6, -2, -14, 2, -2, 16, 4, -18, 6, 0, -8, -6, -6, -14, 18, -14, 0, 16, 0, -24, -2, 10, -6, -24, -16, -12, -8, 16, -12, 24, -4, 8, -16, -24, -20, 12, -16, -10, -2, 14, 22, 16, 4, 24, 28, 12, -8, 16, -8, -12, 24, 8, -12, 26, -26, 14, 18, 0, -20, -2, -18, 22, -26, -14, -14, -36, -24, 0, 28, 14, -34, 24, -4, -4, -12, -14, 18, 34, -14, -24, -12, -12, -16, -6, -14, 14, -34, 28, 20, 36, -8, -34, 30, -10, -26, 10, -6, 2, 2, 14, 46, -34, -34, -24, 36, -28, 44, 4, 12, -40, -16, -48, 16, -16, -24, 2, -30, -24, -16, -10, 30, 18, -46, 0, 52, -44, 24, -26, -42, 52, 24, -8, 20, 48, 28, -20, -8, -38, -30, -30, 42, -18, 22, -52, 0, -4, 16, 32, -36, -14, -46] 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^2+w+2])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]