/* 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, 0, -5, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([4, 2, w^2 - w - 2]) primes_array = [ [2, 2, w],\ [2, 2, w + 1],\ [13, 13, -w^2 + w + 3],\ [13, 13, w^2 + w - 3],\ [19, 19, -w^3 + 3*w + 1],\ [19, 19, -w^3 + 3*w - 1],\ [43, 43, -w^2 + w - 1],\ [43, 43, w^2 + w + 1],\ [49, 7, w^3 + w^2 - 6*w - 3],\ [49, 7, w^3 - w^2 - 6*w + 3],\ [53, 53, 2*w^3 - w^2 - 9*w + 3],\ [53, 53, 2*w^3 + w^2 - 9*w - 3],\ [59, 59, w^3 - w^2 - 4*w + 1],\ [59, 59, -w^3 - w^2 + 4*w + 1],\ [67, 67, 3*w^3 - 13*w + 1],\ [67, 67, -w^3 + w^2 + 6*w - 5],\ [81, 3, -3],\ [83, 83, -2*w^3 - w^2 + 9*w + 7],\ [83, 83, 4*w^3 - 18*w - 1],\ [89, 89, -2*w^3 + 10*w + 1],\ [89, 89, -w^2 + w + 5],\ [89, 89, w^2 + w - 5],\ [89, 89, 2*w^3 - 10*w + 1],\ [101, 101, -2*w^3 + 8*w + 1],\ [101, 101, 2*w^3 - 8*w + 1],\ [103, 103, w^3 + 2*w^2 - 5*w - 7],\ [103, 103, w^3 + w^2 - 6*w - 7],\ [103, 103, -w^2 - 3*w + 1],\ [103, 103, -w^3 + 2*w^2 + 5*w - 7],\ [127, 127, -w^3 + 2*w^2 + 5*w - 5],\ [127, 127, w^3 + 3*w^2 - 4*w - 13],\ [127, 127, -w^3 + 3*w^2 + 4*w - 13],\ [127, 127, w^3 + 2*w^2 - 5*w - 5],\ [149, 149, -2*w^3 - w^2 + 7*w - 1],\ [149, 149, 2*w^3 - w^2 - 7*w - 1],\ [151, 151, -w^3 + w^2 + 2*w - 3],\ [151, 151, 2*w^3 - 10*w + 3],\ [151, 151, -2*w^3 + 10*w + 3],\ [151, 151, w^3 + w^2 - 2*w - 3],\ [157, 157, w^3 + 2*w^2 - 3*w - 1],\ [157, 157, -w^3 + 2*w^2 + 3*w - 1],\ [169, 13, 2*w^2 - 3],\ [179, 179, 2*w^3 + w^2 - 7*w - 3],\ [179, 179, -2*w^3 + w^2 + 7*w - 3],\ [229, 229, -w^3 + 2*w^2 + 3*w - 7],\ [229, 229, w^3 + 2*w^2 - 3*w - 7],\ [251, 251, -2*w^3 + 2*w^2 + 8*w - 9],\ [251, 251, -2*w^3 - 2*w^2 + 8*w + 9],\ [263, 263, 2*w^3 - w^2 - 3*w + 1],\ [263, 263, -2*w^3 + 2*w^2 + 10*w - 5],\ [263, 263, -2*w^3 - 2*w^2 + 10*w + 5],\ [263, 263, -2*w^3 - w^2 + 3*w + 1],\ [289, 17, 2*w^2 - 5],\ [293, 293, 4*w^3 - w^2 - 19*w + 7],\ [293, 293, -4*w^3 - w^2 + 19*w + 7],\ [307, 307, -w^3 + 3*w - 5],\ [307, 307, w^3 - 3*w - 5],\ [331, 331, 4*w^3 - 2*w^2 - 18*w + 7],\ [331, 331, 5*w^3 - 3*w^2 - 22*w + 11],\ [349, 349, -3*w^3 + 13*w + 3],\ [349, 349, -3*w^3 + 13*w - 3],\ [361, 19, 2*w^2 - 11],\ [373, 373, w^3 + 2*w^2 + w - 3],\ [373, 373, -w^3 + 2*w^2 - w - 3],\ [383, 383, -w^3 + 5*w + 5],\ [383, 383, -3*w^3 + 2*w^2 + 11*w - 5],\ [383, 383, 3*w^3 + 2*w^2 - 11*w - 5],\ [383, 383, w^3 - 5*w + 5],\ [389, 389, w^3 - 4*w^2 + w + 7],\ [389, 389, -2*w^3 - w^2 + 7*w + 7],\ [421, 421, -w^3 - w^2 - 2*w + 1],\ [421, 421, w^3 - w^2 + 2*w + 1],\ [433, 433, 4*w^3 - 2*w^2 - 16*w + 5],\ [433, 433, -4*w + 1],\ [433, 433, 4*w + 1],\ [433, 433, -5*w^3 + 3*w^2 + 24*w - 13],\ [443, 443, -w^3 + w^2 + 3],\ [443, 443, -4*w^2 + 6*w + 7],\ [457, 457, 3*w^3 + w^2 - 12*w - 3],\ [457, 457, -2*w^3 + 6*w - 1],\ [457, 457, 2*w^3 - 6*w - 1],\ [457, 457, 3*w^3 - w^2 - 12*w + 3],\ [461, 461, w^3 - 3*w^2 - 2*w + 7],\ [461, 461, w^3 + 3*w^2 - 2*w - 7],\ [463, 463, -2*w^3 + 3*w^2 + 9*w - 11],\ [463, 463, 2*w^3 - w^2 - 5*w + 1],\ [463, 463, -2*w^3 - w^2 + 5*w + 1],\ [463, 463, -2*w^3 - 3*w^2 + 9*w + 11],\ [467, 467, w^3 - 7*w + 1],\ [467, 467, -w^3 + 7*w + 1],\ [491, 491, 2*w^2 - 2*w - 7],\ [491, 491, 2*w^2 + 2*w - 7],\ [509, 509, w^3 + 3*w^2 - 4*w - 11],\ [509, 509, -w^3 + 3*w^2 + 4*w - 11],\ [523, 523, 2*w^3 - w^2 - 11*w + 3],\ [523, 523, 2*w^3 + w^2 - 11*w - 3],\ [529, 23, 3*w^2 - w - 15],\ [529, 23, -3*w^2 - w + 15],\ [557, 557, 3*w^2 + w - 13],\ [557, 557, -3*w^2 + w + 13],\ [563, 563, -3*w^3 + 3*w^2 + 12*w - 7],\ [563, 563, 2*w^3 - 2*w^2 - 8*w + 3],\ [569, 569, w^3 + 3*w^2 - 6*w - 9],\ [569, 569, 4*w^3 - w^2 - 17*w + 1],\ [569, 569, -4*w^3 - w^2 + 17*w + 1],\ [569, 569, -w^3 + 3*w^2 + 6*w - 9],\ [587, 587, -w^3 + w^2 + 2*w - 5],\ [587, 587, w^3 + w^2 - 2*w - 5],\ [593, 593, 3*w^3 - 2*w^2 - 15*w + 5],\ [593, 593, -w^3 - 2*w^2 + 5*w + 1],\ [593, 593, w^3 - 2*w^2 - 5*w + 1],\ [593, 593, -3*w^3 - 2*w^2 + 15*w + 5],\ [599, 599, w^3 + w^2 - 3],\ [599, 599, -w^2 - w - 3],\ [599, 599, -w^2 + w - 3],\ [599, 599, -w^3 + w^2 - 3],\ [613, 613, -w^3 + w^2 + 6*w - 9],\ [613, 613, w^3 + w^2 - 6*w - 9],\ [625, 5, -5],\ [659, 659, -2*w^3 + 4*w^2 + 4*w - 1],\ [659, 659, 2*w^3 + 4*w^2 - 4*w - 1],\ [661, 661, w^3 + 3*w^2 - 6*w - 7],\ [661, 661, -2*w^3 + 6*w^2 - 7],\ [701, 701, -w^3 - 2*w^2 + 3*w + 9],\ [701, 701, -w^3 + 2*w^2 + 3*w - 9],\ [733, 733, w^3 + 2*w^2 - 7*w - 1],\ [733, 733, -4*w^3 + w^2 + 19*w - 11],\ [739, 739, -w^3 - w^2 + 2*w + 9],\ [739, 739, -w^3 + w^2 + 2*w - 9],\ [757, 757, 3*w^3 - w^2 - 10*w + 5],\ [757, 757, -3*w^3 - w^2 + 10*w + 5],\ [773, 773, -4*w^3 + 5*w^2 + 19*w - 23],\ [773, 773, -7*w^3 + 6*w^2 + 33*w - 29],\ [797, 797, 3*w^3 - 13*w + 5],\ [797, 797, 3*w^3 - 13*w - 5],\ [829, 829, -2*w^3 - w^2 + 9*w - 1],\ [829, 829, 2*w^3 - w^2 - 9*w - 1],\ [859, 859, 3*w^3 - w^2 - 14*w + 1],\ [859, 859, -3*w^3 - w^2 + 14*w + 1],\ [863, 863, -5*w^3 + 21*w + 3],\ [863, 863, -3*w^3 - w^2 + 12*w - 1],\ [863, 863, 3*w^3 - w^2 - 12*w - 1],\ [863, 863, -5*w^3 + 21*w - 3],\ [883, 883, -2*w^3 + 4*w^2 + 8*w - 17],\ [883, 883, 2*w^3 + 4*w^2 - 8*w - 17],\ [953, 953, -w^3 - w^2 + 8*w + 3],\ [953, 953, 4*w^3 - 2*w^2 - 16*w + 7],\ [953, 953, -3*w^3 + w^2 + 16*w - 7],\ [953, 953, w^3 - w^2 - 8*w + 3],\ [961, 31, -4*w^3 + 2*w^2 + 12*w + 3],\ [961, 31, 3*w^3 - w^2 - 10*w - 1],\ [971, 971, 3*w^3 - 4*w^2 - 13*w + 15],\ [971, 971, -4*w^3 + 3*w^2 + 19*w - 17],\ [977, 977, -2*w^3 + w^2 + 9*w + 3],\ [977, 977, -4*w^3 + w^2 + 19*w - 9],\ [977, 977, 3*w^3 - 15*w + 5],\ [977, 977, 2*w^3 + w^2 - 9*w + 3]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [1, 1, -2, -2, 4, 4, -4, -4, -14, -14, 6, 6, 12, 12, 4, 4, -14, -12, -12, -6, -6, -6, -6, 6, 6, 8, -8, -8, 8, -16, 16, 16, -16, 6, 6, -8, 8, 8, -8, 14, 14, -22, -12, -12, 22, 22, 12, 12, -24, 24, 24, -24, 2, 6, 6, 20, 20, -4, -4, -34, -34, -22, 22, 22, 0, 0, 0, 0, 6, 6, -26, -26, -14, -14, -14, -14, 12, 12, 10, 10, 10, 10, -18, -18, 32, -32, -32, 32, 36, 36, 12, 12, -18, -18, -20, -20, -14, -14, -18, -18, 36, 36, -6, -6, -6, -6, 12, 12, 18, 18, 18, 18, -24, 24, 24, -24, -10, -10, -46, -12, -12, -10, -10, 30, 30, 14, 14, -44, -44, 22, 22, 54, 54, -18, -18, -34, -34, -4, -4, 48, -48, -48, 48, -44, -44, -6, -6, -6, -6, -62, -62, 12, 12, 18, 18, 18, 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]