/* 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, -4, -1, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([145,145,w^3 - 4*w - 3]) primes_array = [ [5, 5, -w^2 + 1],\ [9, 3, w^3 + w^2 - 4*w - 3],\ [16, 2, 2],\ [29, 29, -w^3 - w^2 + 2*w + 3],\ [29, 29, -w^2 + w + 3],\ [29, 29, w^3 - w^2 - 4*w + 2],\ [29, 29, 2*w^3 + w^2 - 7*w],\ [31, 31, -2*w + 1],\ [31, 31, 2*w^2 - 5],\ [31, 31, 2*w^3 + 2*w^2 - 6*w - 3],\ [31, 31, 2*w^3 - 8*w + 1],\ [59, 59, w^3 + w^2 - 2*w - 5],\ [59, 59, -w^3 + 2*w^2 + 4*w - 5],\ [59, 59, -3*w^3 + 10*w - 4],\ [59, 59, -2*w^3 - w^2 + 7*w - 2],\ [61, 61, 4*w^3 + w^2 - 13*w - 1],\ [61, 61, 2*w^3 - w^2 - 5*w + 2],\ [61, 61, -3*w^3 - w^2 + 8*w],\ [61, 61, 3*w^3 - w^2 - 10*w + 5],\ [89, 89, w^3 + w^2 - w - 4],\ [89, 89, 2*w^2 - w - 6],\ [89, 89, -3*w^3 - 2*w^2 + 10*w + 1],\ [89, 89, -2*w^3 + w^2 + 8*w - 2],\ [121, 11, -w^3 + 3*w + 3],\ [121, 11, 3*w^3 - 9*w + 1],\ [149, 149, 3*w^3 + 2*w^2 - 9*w - 5],\ [149, 149, w^3 + 2*w^2 - 2*w - 7],\ [149, 149, w^3 + w^2 - 5*w - 4],\ [149, 149, -3*w^3 + 11*w - 4],\ [151, 151, 3*w^3 - w^2 - 9*w + 3],\ [151, 151, 3*w^3 - 8*w + 2],\ [151, 151, 4*w^3 + w^2 - 12*w - 1],\ [151, 151, -4*w^3 + 13*w - 3],\ [179, 179, -4*w^3 - w^2 + 14*w - 1],\ [179, 179, 3*w^3 + 2*w^2 - 8*w - 4],\ [179, 179, -w^3 + w^2 + w - 3],\ [179, 179, -2*w^3 + 2*w^2 + 7*w - 5],\ [181, 181, 4*w^3 + w^2 - 12*w],\ [181, 181, -3*w^3 + 8*w - 1],\ [181, 181, 4*w^3 - 13*w + 2],\ [181, 181, -3*w^3 + w^2 + 9*w - 4],\ [211, 211, 2*w^3 + 3*w^2 - 6*w - 6],\ [211, 211, -w^3 + 6*w - 2],\ [211, 211, 2*w^3 - 9*w + 2],\ [211, 211, 2*w^3 + 3*w^2 - 6*w - 5],\ [239, 239, w^3 + 3*w^2 - 2*w - 10],\ [239, 239, 2*w^3 + w^2 - 9*w - 4],\ [239, 239, 2*w^3 + w^2 - 9*w + 3],\ [239, 239, -w^3 - 3*w^2 + 2*w + 3],\ [241, 241, 5*w^3 + w^2 - 16*w - 1],\ [241, 241, -2*w^3 - 4*w^2 + 5*w + 9],\ [241, 241, 3*w^3 + w^2 - 13*w + 1],\ [241, 241, 5*w^3 - 16*w],\ [269, 269, -3*w^3 - 2*w^2 + 7*w + 4],\ [269, 269, -2*w^3 - 3*w^2 + 5*w + 8],\ [269, 269, -3*w^3 - 2*w^2 + 9*w + 7],\ [269, 269, 5*w^3 + 2*w^2 - 17*w - 1],\ [271, 271, 5*w^3 + w^2 - 16*w],\ [271, 271, -2*w^3 - w^2 + 6*w + 6],\ [271, 271, 4*w^3 + w^2 - 11*w],\ [271, 271, 3*w^3 - w^2 - 8*w + 3],\ [331, 331, -w^3 + 2*w^2 + 6*w - 6],\ [331, 331, -2*w^3 - 3*w^2 + 7*w + 5],\ [331, 331, 2*w^3 + 3*w^2 - 8*w - 5],\ [331, 331, 3*w^3 + 3*w^2 - 11*w - 5],\ [359, 359, 2*w^3 + 2*w^2 - 9*w - 5],\ [359, 359, 3*w^3 + 2*w^2 - 12*w],\ [359, 359, w^3 + 3*w^2 - w - 9],\ [359, 359, 3*w^2 + 2*w - 5],\ [361, 19, -w^3 + 3*w + 4],\ [361, 19, 4*w^3 - 12*w + 1],\ [389, 389, w^3 - 3*w^2 - 3*w + 5],\ [389, 389, 2*w^3 + 2*w^2 - 5*w - 7],\ [389, 389, 4*w^3 + 3*w^2 - 12*w - 7],\ [389, 389, -4*w^3 + 15*w - 5],\ [419, 419, -3*w^3 - 3*w^2 + 8*w + 7],\ [419, 419, -4*w^3 - 2*w^2 + 13*w - 1],\ [419, 419, -4*w^3 - w^2 + 15*w - 2],\ [419, 419, w^3 - 3*w^2 - 4*w + 6],\ [421, 421, w^2 - 7],\ [421, 421, -w^3 + 4*w + 4],\ [421, 421, 4*w^3 - 11*w],\ [421, 421, 4*w^3 - w^2 - 12*w + 6],\ [449, 449, 3*w^3 + 2*w^2 - 11*w + 1],\ [449, 449, -w^3 - 2*w^2 + 5*w + 7],\ [449, 449, -w^3 + 2*w^2 + 5*w - 2],\ [449, 449, w^3 + 2*w^2 - w - 8],\ [479, 479, 2*w^3 + 3*w^2 - 5*w - 9],\ [479, 479, -3*w^2 - w + 4],\ [479, 479, -3*w^3 - w^2 + 12*w - 3],\ [479, 479, w^3 + w^2 - 6*w - 4],\ [509, 509, 4*w^3 + 3*w^2 - 11*w - 6],\ [509, 509, -w^3 + w^2 - 3],\ [509, 509, -2*w^3 + 3*w^2 + 7*w - 7],\ [509, 509, -5*w^3 - w^2 + 18*w - 2],\ [541, 541, -4*w^3 + 11*w - 2],\ [541, 541, -4*w^3 + w^2 + 12*w - 4],\ [541, 541, 5*w^3 - 16*w + 3],\ [541, 541, 5*w^3 + w^2 - 15*w],\ [569, 569, -4*w^3 - w^2 + 14*w - 3],\ [569, 569, 4*w^3 + 2*w^2 - 15*w],\ [569, 569, w^3 - 3*w^2 - 5*w + 6],\ [569, 569, 2*w^3 + 3*w^2 - 4*w - 8],\ [571, 571, -4*w^3 - w^2 + 17*w + 2],\ [571, 571, 3*w^3 + 4*w^2 - 10*w - 10],\ [571, 571, w^3 + 5*w^2 - 2*w - 14],\ [571, 571, -6*w^3 + 20*w - 3],\ [599, 599, -2*w^3 + w^2 + 4*w - 5],\ [599, 599, -4*w^3 - 2*w^2 + 11*w + 5],\ [599, 599, 3*w^3 - 2*w^2 - 10*w + 4],\ [599, 599, -5*w^3 - w^2 + 17*w - 3],\ [601, 601, w^3 - 7*w + 1],\ [601, 601, 3*w^3 + 4*w^2 - 9*w - 8],\ [601, 601, 3*w^3 - 13*w + 3],\ [601, 601, w^3 + 4*w^2 - 3*w - 8],\ [631, 631, 6*w^3 + w^2 - 19*w - 1],\ [631, 631, -3*w^3 + w^2 + 13*w - 3],\ [631, 631, 5*w^3 + w^2 - 14*w + 2],\ [631, 631, -5*w^3 + w^2 + 16*w - 7],\ [659, 659, -6*w^3 - 2*w^2 + 19*w - 2],\ [659, 659, -5*w^3 + w^2 + 17*w - 2],\ [659, 659, -4*w^3 + 15*w - 6],\ [659, 659, -4*w^3 - 3*w^2 + 12*w + 8],\ [661, 661, -5*w^3 + 2*w^2 + 16*w - 7],\ [661, 661, 6*w^3 + 2*w^2 - 17*w - 2],\ [661, 661, -7*w^3 - w^2 + 23*w - 2],\ [661, 661, -4*w^3 + w^2 + 10*w - 4],\ [691, 691, -6*w^3 + 19*w - 6],\ [691, 691, -5*w^3 + w^2 + 15*w - 2],\ [691, 691, 5*w^3 - 14*w + 5],\ [691, 691, 2*w^3 + 4*w^2 - 7*w - 10],\ [719, 719, -7*w^3 - 2*w^2 + 24*w],\ [719, 719, -2*w^3 + 2*w^2 + 3*w - 5],\ [719, 719, -5*w^3 - 3*w^2 + 13*w + 5],\ [719, 719, -4*w^3 + 3*w^2 + 14*w - 9],\ [751, 751, 4*w^3 + 4*w^2 - 14*w - 5],\ [751, 751, 5*w^3 + 4*w^2 - 17*w - 8],\ [751, 751, -3*w^3 + 2*w^2 + 13*w - 9],\ [751, 751, 6*w^3 + w^2 - 19*w],\ [809, 809, w^3 + 3*w^2 - w - 11],\ [809, 809, -5*w^3 + 18*w - 6],\ [809, 809, -6*w^3 - w^2 + 20*w - 4],\ [809, 809, 5*w^3 + 3*w^2 - 15*w - 7],\ [811, 811, 5*w^3 + 4*w^2 - 18*w - 6],\ [811, 811, 7*w^3 + 2*w^2 - 22*w - 1],\ [811, 811, 4*w^3 - 2*w^2 - 11*w + 6],\ [811, 811, 5*w^3 + w^2 - 13*w],\ [839, 839, -4*w^3 - 4*w^2 + 11*w + 9],\ [839, 839, 5*w^3 + w^2 - 19*w + 3],\ [839, 839, -6*w^3 - 2*w^2 + 21*w],\ [839, 839, -5*w^3 - 3*w^2 + 16*w],\ [929, 929, 5*w^3 + w^2 - 17*w + 4],\ [929, 929, 3*w^3 - 2*w^2 - 10*w + 3],\ [929, 929, 4*w^3 + 2*w^2 - 11*w - 6],\ [929, 929, 4*w^3 + 2*w^2 - 15*w + 1],\ [991, 991, 3*w^3 + w^2 - 14*w + 1],\ [991, 991, 2*w^3 + 5*w^2 - 5*w - 11],\ [991, 991, 2*w^3 + 5*w^2 - 5*w - 10],\ [991, 991, 3*w^2 + 4*w - 7]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, -2, 5, 6, -1, 6, -6, 8, 8, -4, -4, 12, -12, 0, 12, -10, -10, 2, -10, 6, -6, 6, 6, 2, -10, -6, 6, 6, 18, 8, 8, 8, 8, -12, 12, 12, -12, 2, -10, 2, 14, -4, 8, -16, -4, 0, 0, -24, -24, 26, 2, -10, -22, -30, 18, 18, 18, -16, 8, 8, 20, -16, -4, -4, 20, -36, 24, 0, -36, -22, 14, 6, 30, -18, 18, -24, -24, 12, 12, -10, 38, 14, -10, 30, -18, -42, -18, 0, 24, -24, 0, 30, -30, 18, 18, -10, -34, -10, 2, -18, 6, -18, -42, -40, -4, -28, -4, -36, 0, -48, -24, 26, 2, 26, 26, 8, -16, -28, -16, 0, 0, -12, 12, 38, -34, -46, 14, 20, 8, -16, 20, -24, 24, -24, 12, -4, -40, 32, -4, 6, 6, 30, -42, -28, 44, 44, -40, -24, -36, 12, 0, 54, 30, -18, 30, 8, -40, -52, -16] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([5,5,-w^3 + 4*w - 2])] = 1 AL_eigenvalues[ZF.ideal([29,29,-w^2 + w + 3])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]