/* 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, 5, -4, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([16, 8, w^2 - 3*w]) primes_array = [ [2, 2, w],\ [2, 2, -w + 1],\ [4, 2, -w^2 + w + 1],\ [19, 19, -w^3 + 5*w + 3],\ [19, 19, w^3 - 3*w^2 - 2*w + 7],\ [43, 43, -w^3 + 3*w^2 + 2*w - 5],\ [43, 43, -w^3 + w^2 + 2*w - 1],\ [43, 43, w^3 - 2*w^2 - w + 1],\ [43, 43, -w^3 + 5*w + 1],\ [47, 47, -w^3 + w^2 + 2*w + 1],\ [47, 47, w^3 - 5*w - 5],\ [47, 47, -w^3 + 3*w^2 + 2*w - 9],\ [47, 47, w^3 - 2*w^2 - w + 3],\ [49, 7, -w^3 + w^2 + 6*w + 1],\ [49, 7, -w^3 + 2*w^2 + 5*w - 7],\ [53, 53, 2*w - 1],\ [67, 67, -w^3 + w^2 + 4*w - 3],\ [67, 67, -w^3 + 2*w^2 + 3*w - 1],\ [81, 3, -3],\ [83, 83, 2*w^3 - 4*w^2 - 6*w + 9],\ [83, 83, -2*w^3 + 2*w^2 + 8*w + 1],\ [101, 101, w^3 - 2*w^2 - 5*w + 3],\ [101, 101, 4*w^3 - 10*w^2 - 12*w + 25],\ [103, 103, -2*w^3 + 4*w^2 + 6*w - 7],\ [103, 103, -2*w^3 + 2*w^2 + 8*w - 1],\ [121, 11, -w^3 + 4*w^2 + w - 13],\ [121, 11, w^3 + w^2 - 6*w - 9],\ [127, 127, -4*w^3 + 4*w^2 + 18*w - 1],\ [127, 127, 4*w^3 - 8*w^2 - 14*w + 17],\ [137, 137, w^3 - 2*w^2 - 5*w + 1],\ [137, 137, -w^3 + w^2 + 6*w - 5],\ [151, 151, 2*w^3 - 4*w^2 - 8*w + 9],\ [151, 151, -3*w^3 + 8*w^2 + 9*w - 21],\ [157, 157, 2*w^3 - 2*w^2 - 10*w + 3],\ [157, 157, -2*w^3 + 4*w^2 + 8*w - 7],\ [169, 13, 2*w^2 - 2*w - 7],\ [169, 13, 2*w^2 - 2*w - 3],\ [179, 179, -w^3 + w^2 + 6*w - 1],\ [179, 179, -w^3 + 2*w^2 + 5*w - 5],\ [191, 191, 5*w^3 - 11*w^2 - 16*w + 27],\ [191, 191, -5*w^3 + 4*w^2 + 23*w + 5],\ [223, 223, 2*w^2 - 4*w - 5],\ [223, 223, w^3 - 3*w - 3],\ [223, 223, -w^3 + 3*w^2 - 5],\ [223, 223, 3*w^3 - 3*w^2 - 14*w - 3],\ [229, 229, 2*w^3 - 4*w^2 - 6*w + 5],\ [229, 229, w^3 - 4*w^2 - w + 11],\ [229, 229, w^3 + w^2 - 6*w - 7],\ [229, 229, -2*w^3 + 2*w^2 + 8*w - 3],\ [239, 239, -3*w^3 + 4*w^2 + 13*w - 3],\ [239, 239, 3*w^3 - 5*w^2 - 12*w + 11],\ [251, 251, -2*w^3 + 4*w^2 + 4*w - 7],\ [251, 251, -2*w^3 + 2*w^2 + 6*w + 1],\ [257, 257, -3*w^3 + 8*w^2 + 7*w - 19],\ [257, 257, 3*w^3 - w^2 - 14*w - 7],\ [263, 263, -w^3 + 7*w - 1],\ [263, 263, -w^3 + 3*w^2 + 4*w - 5],\ [281, 281, -w^3 + 7*w + 5],\ [281, 281, w^3 - 5*w + 1],\ [281, 281, -w^3 + 3*w^2 + 2*w - 3],\ [281, 281, w^3 - 3*w^2 - 4*w + 11],\ [289, 17, 2*w^2 - 2*w - 5],\ [349, 349, -3*w^3 + 2*w^2 + 15*w + 7],\ [349, 349, 3*w^3 - 7*w^2 - 10*w + 21],\ [353, 353, w^3 - 4*w^2 - w + 5],\ [353, 353, -w^3 - w^2 + 6*w + 1],\ [359, 359, -2*w^2 + 6*w + 3],\ [359, 359, -2*w^2 - 2*w + 7],\ [361, 19, 2*w^2 - 2*w + 1],\ [373, 373, 2*w^3 - 12*w - 9],\ [373, 373, -2*w^3 + 6*w^2 + 6*w - 19],\ [383, 383, -5*w^3 + 2*w^2 + 25*w + 13],\ [383, 383, -5*w^3 + 13*w^2 + 14*w - 35],\ [389, 389, 2*w^3 - 8*w - 5],\ [389, 389, 2*w^3 - 6*w^2 - 2*w + 11],\ [421, 421, -4*w^3 + 2*w^2 + 20*w + 11],\ [421, 421, -4*w^3 + 10*w^2 + 12*w - 29],\ [443, 443, w^3 - w^2 - 8*w - 5],\ [443, 443, w^3 - 2*w^2 - 7*w + 13],\ [457, 457, w^3 - w - 3],\ [457, 457, w^3 - 3*w^2 + 2*w + 3],\ [463, 463, w^3 - 4*w^2 - 3*w + 13],\ [463, 463, w^3 + w^2 - 8*w - 7],\ [467, 467, w^3 - 4*w^2 - w + 9],\ [467, 467, w^3 - 4*w^2 - 3*w + 17],\ [467, 467, w^3 + w^2 - 8*w - 11],\ [467, 467, w^3 + w^2 - 6*w - 5],\ [491, 491, 9*w^3 - 19*w^2 - 30*w + 47],\ [491, 491, -3*w^3 + 9*w^2 + 8*w - 29],\ [509, 509, -5*w^3 + 4*w^2 + 25*w + 5],\ [509, 509, 5*w^3 - 11*w^2 - 18*w + 29],\ [523, 523, -3*w^3 + 4*w^2 + 13*w - 7],\ [523, 523, -3*w^3 + 3*w^2 + 12*w + 1],\ [523, 523, 3*w^3 - 6*w^2 - 9*w + 13],\ [523, 523, -3*w^3 + 5*w^2 + 12*w - 7],\ [557, 557, 2*w - 7],\ [557, 557, -2*w - 5],\ [563, 563, 4*w^3 - 10*w^2 - 12*w + 23],\ [563, 563, -4*w^3 + 2*w^2 + 20*w + 5],\ [569, 569, 2*w^3 - 10*w - 9],\ [569, 569, -2*w^3 + 6*w^2 + 4*w - 17],\ [577, 577, 2*w^3 - 2*w^2 - 6*w - 3],\ [577, 577, 3*w^3 - 7*w^2 - 12*w + 23],\ [577, 577, 3*w^3 - 3*w^2 - 10*w + 7],\ [577, 577, -2*w^3 + 4*w^2 + 4*w - 9],\ [587, 587, 3*w^3 - w^2 - 16*w - 11],\ [587, 587, 5*w^3 - 9*w^2 - 18*w + 17],\ [587, 587, -5*w^3 + 6*w^2 + 21*w - 5],\ [587, 587, 3*w^3 - 8*w^2 - 9*w + 25],\ [613, 613, -3*w^3 + 6*w^2 + 9*w - 11],\ [613, 613, 3*w^3 - 3*w^2 - 12*w + 1],\ [625, 5, -5],\ [631, 631, -2*w^3 + 4*w^2 + 4*w - 5],\ [631, 631, -2*w^3 + 2*w^2 + 6*w - 1],\ [659, 659, -4*w^3 + 6*w^2 + 16*w - 11],\ [659, 659, -4*w^3 + 6*w^2 + 16*w - 7],\ [661, 661, -2*w^3 + 6*w^2 + 4*w - 19],\ [661, 661, 5*w^3 - 2*w^2 - 25*w - 15],\ [661, 661, 5*w^3 - 13*w^2 - 14*w + 37],\ [661, 661, -3*w^3 + w^2 + 10*w + 1],\ [701, 701, 3*w^3 - 7*w^2 - 10*w + 15],\ [701, 701, -3*w^3 + 2*w^2 + 15*w + 1],\ [727, 727, 2*w^3 - 2*w^2 - 4*w + 1],\ [727, 727, -4*w + 7],\ [727, 727, -4*w - 3],\ [727, 727, 2*w^3 - 4*w^2 - 2*w + 3],\ [739, 739, -w^3 + 2*w^2 - w + 3],\ [739, 739, -2*w^3 + 2*w^2 + 12*w - 7],\ [757, 757, -3*w^3 + 3*w^2 + 14*w - 3],\ [757, 757, w^3 + 4*w^2 - 9*w - 23],\ [757, 757, -w^3 + 7*w^2 - 2*w - 27],\ [757, 757, -3*w^3 + 6*w^2 + 11*w - 11],\ [761, 761, 4*w - 1],\ [761, 761, 4*w - 3],\ [769, 769, -w^3 + 3*w^2 + 4*w - 3],\ [769, 769, -w^3 + 7*w - 3],\ [773, 773, w^3 - w^2 - 4*w - 5],\ [773, 773, -w^3 + 2*w^2 + 3*w - 9],\ [797, 797, -3*w^3 + w^2 + 14*w + 3],\ [797, 797, 3*w^3 - 8*w^2 - 7*w + 15],\ [829, 829, -w^3 + 3*w^2 - 7],\ [829, 829, w^3 - 3*w - 5],\ [841, 29, -w^3 + w^2 + 8*w - 7],\ [841, 29, w^3 - 2*w^2 - 7*w + 1],\ [863, 863, 2*w^2 - 4*w - 7],\ [863, 863, -5*w^3 + 4*w^2 + 25*w + 3],\ [863, 863, 5*w^3 - 11*w^2 - 18*w + 27],\ [863, 863, 2*w^2 - 9],\ [883, 883, 2*w^3 - 2*w^2 - 10*w - 5],\ [883, 883, -2*w^3 + 4*w^2 + 8*w - 15],\ [919, 919, w^3 + w^2 - 4*w - 7],\ [919, 919, -w^3 + 4*w^2 - w - 9],\ [937, 937, 3*w^3 - 4*w^2 - 11*w + 5],\ [937, 937, w^3 + w^2 - 8*w - 9],\ [937, 937, -w^3 + 4*w^2 + 3*w - 15],\ [937, 937, -3*w^3 + 5*w^2 + 10*w - 7],\ [953, 953, w^3 - 2*w^2 - 3*w - 3],\ [953, 953, 5*w^3 - 11*w^2 - 18*w + 33],\ [953, 953, 3*w^3 - 3*w^2 - 10*w + 5],\ [953, 953, -w^3 + w^2 + 4*w - 7],\ [971, 971, -w^3 + 7*w - 5],\ [971, 971, 3*w^3 - 5*w^2 - 10*w + 3],\ [971, 971, -3*w^3 + 4*w^2 + 11*w - 9],\ [971, 971, w^3 - 3*w^2 - 4*w + 1],\ [977, 977, -2*w^3 + 2*w^2 + 10*w - 5],\ [977, 977, 2*w^3 - 4*w^2 - 8*w + 5]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 0, 0, -3, -7, -7, 6, -2, 1, 5, 7, 3, -3, 9, 5, 2, 14, 6, -7, 8, 16, -3, -15, 6, 6, 2, 2, 22, -18, -20, 12, 16, -8, -4, 12, -6, -10, -7, -11, -21, -25, -28, 7, -9, 28, 29, -4, -4, 17, 8, 16, 14, -2, 16, 8, 2, 2, 18, 6, -18, -30, -11, -10, -2, -12, 12, -11, 13, 9, 14, 30, -6, 10, 6, 6, -17, 19, -5, -9, -7, 13, -12, -4, 12, 18, 18, -12, -10, 30, -3, 13, 31, 26, 2, -21, 34, -6, 21, 5, 45, -11, 32, -14, 10, -16, 4, -12, 12, 36, 37, -11, -2, 20, 20, -12, -12, -35, 10, 10, 21, 14, -2, 13, -23, -23, -47, -9, -13, -5, -12, 52, 47, 32, 32, -44, -4, -21, -1, 4, 28, 18, 34, -42, 6, 28, -10, -2, 12, 20, 12, 27, 19, -26, -30, -46, 14, -14, 1, 21, -14, -26, -23, -15, 30, -30, 18] 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]