/* 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([4, 0, -6, 0, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([71,71,1/2*w^3 - 1/2*w^2 - 2*w - 2]) primes_array = [ [4, 2, 1/2*w^3 - 2*w],\ [9, 3, -1/2*w^3 + 1/2*w^2 + 2*w - 3],\ [9, 3, 1/2*w^3 + 1/2*w^2 - 2*w - 3],\ [25, 5, w^2 - 3],\ [31, 31, 1/2*w^3 + 1/2*w^2 - 3*w],\ [31, 31, -1/2*w^2 - w + 3],\ [31, 31, -1/2*w^2 + w + 3],\ [31, 31, 1/2*w^3 - 1/2*w^2 - 3*w],\ [41, 41, 1/2*w^3 - w^2 - w + 3],\ [41, 41, w^3 + w^2 - 5*w - 3],\ [41, 41, -3/2*w^2 - w + 5],\ [41, 41, -1/2*w^3 - w^2 + w + 3],\ [49, 7, -1/2*w^3 + 2*w - 3],\ [49, 7, 1/2*w^3 - 2*w - 3],\ [71, 71, 1/2*w^3 + 1/2*w^2 - 2*w - 5],\ [71, 71, 1/2*w^3 + 3/2*w^2 - 3*w - 5],\ [71, 71, 1/2*w^3 - 3/2*w^2 - 3*w + 5],\ [71, 71, -1/2*w^3 + 1/2*w^2 + 2*w - 5],\ [79, 79, 1/2*w^3 + 3/2*w^2 - 2*w - 4],\ [79, 79, -w^3 - 1/2*w^2 + 6*w],\ [79, 79, w^3 - 1/2*w^2 - 6*w],\ [79, 79, 1/2*w^3 - 3/2*w^2 - 2*w + 4],\ [89, 89, w^2 + w - 5],\ [89, 89, -w^3 + 1/2*w^2 + 5*w],\ [89, 89, w^3 + 1/2*w^2 - 5*w],\ [89, 89, w^2 - w - 5],\ [121, 11, 3/2*w^2 - 5],\ [121, 11, 1/2*w^2 - 5],\ [151, 151, -w^3 + 1/2*w^2 + 5*w + 1],\ [151, 151, 1/2*w^3 + 1/2*w^2 - w - 4],\ [151, 151, -1/2*w^3 + 1/2*w^2 + w - 4],\ [151, 151, -w^3 - 1/2*w^2 + 5*w - 1],\ [169, 13, -1/2*w^3 - 2*w^2 + 3*w + 3],\ [169, 13, 2*w^2 - w - 9],\ [191, 191, -w^3 - 2*w^2 + 5*w + 7],\ [191, 191, 3/2*w^3 - 1/2*w^2 - 5*w + 3],\ [191, 191, -3/2*w^3 - 1/2*w^2 + 5*w + 3],\ [191, 191, w^3 - 2*w^2 - 5*w + 7],\ [199, 199, -1/2*w^3 + w^2 + 4*w - 7],\ [199, 199, -3/2*w^3 + 3/2*w^2 + 7*w - 4],\ [199, 199, 3/2*w^3 + 3/2*w^2 - 7*w - 4],\ [199, 199, 1/2*w^3 + w^2 - 4*w - 7],\ [239, 239, 2*w^3 - w^2 - 9*w + 3],\ [239, 239, -3/2*w^3 - w^2 + 5*w + 3],\ [239, 239, 3/2*w^3 - w^2 - 5*w + 3],\ [239, 239, 2*w^3 + w^2 - 9*w - 3],\ [241, 241, -w^3 + w^2 + 5*w - 1],\ [241, 241, -1/2*w^3 + w^2 + w - 5],\ [241, 241, 1/2*w^3 + w^2 - w - 5],\ [241, 241, w^3 + w^2 - 5*w - 1],\ [271, 271, 3/2*w^3 - 9*w - 1],\ [271, 271, 3*w - 1],\ [271, 271, -3*w - 1],\ [271, 271, 1/2*w^2 - 3*w],\ [281, 281, 1/2*w^3 + 2*w^2 - 2*w - 7],\ [281, 281, -1/2*w^3 + 1/2*w^2 + 3*w - 6],\ [281, 281, 1/2*w^3 + 1/2*w^2 - 3*w - 6],\ [281, 281, -1/2*w^3 + 2*w^2 + 2*w - 7],\ [289, 17, 1/2*w^2 + 3*w - 1],\ [289, 17, 1/2*w^2 - 3*w - 1],\ [311, 311, w^3 - 1/2*w^2 - 2*w + 3],\ [311, 311, 2*w^3 + 1/2*w^2 - 10*w],\ [311, 311, -2*w^3 + 1/2*w^2 + 10*w],\ [311, 311, -w^3 - 1/2*w^2 + 2*w + 3],\ [359, 359, w^3 - 3/2*w^2 - 6*w + 3],\ [359, 359, -3/2*w^3 - 1/2*w^2 + 7*w - 2],\ [359, 359, 3/2*w^3 - 1/2*w^2 - 7*w - 2],\ [359, 359, w^3 - 1/2*w^2 - 3*w + 5],\ [361, 19, 2*w^2 - 7],\ [361, 19, 1/2*w^2 - 6],\ [401, 401, -2*w^3 - 1/2*w^2 + 9*w + 3],\ [401, 401, 3/2*w^3 + 1/2*w^2 - 5*w],\ [401, 401, -3/2*w^3 + 1/2*w^2 + 5*w],\ [401, 401, 2*w^3 - 1/2*w^2 - 9*w + 3],\ [409, 409, 3/2*w^3 + 3/2*w^2 - 8*w - 4],\ [409, 409, -1/2*w^3 - 3/2*w^2 + 5],\ [409, 409, 1/2*w^3 - 3/2*w^2 + 5],\ [409, 409, -3/2*w^3 + 3/2*w^2 + 8*w - 4],\ [431, 431, -2*w^3 + 9*w + 1],\ [431, 431, -3/2*w^3 + 5*w + 1],\ [431, 431, 3/2*w^3 - 5*w + 1],\ [431, 431, 2*w^3 - 9*w + 1],\ [439, 439, -3/2*w^3 + 1/2*w^2 + 5*w - 1],\ [439, 439, -2*w^3 + 1/2*w^2 + 9*w - 2],\ [439, 439, -2*w^3 - 1/2*w^2 + 9*w + 2],\ [439, 439, -3/2*w^3 - 1/2*w^2 + 5*w + 1],\ [449, 449, -w^3 - 3/2*w^2 + 3*w + 6],\ [449, 449, 3/2*w^3 + 3/2*w^2 - 7*w - 3],\ [449, 449, -3/2*w^3 + 3/2*w^2 + 7*w - 3],\ [449, 449, w^3 - 3/2*w^2 - 3*w + 6],\ [479, 479, -w - 5],\ [479, 479, 1/2*w^3 - 3*w - 5],\ [479, 479, -1/2*w^3 + 3*w - 5],\ [479, 479, w - 5],\ [521, 521, -5/2*w^3 - 1/2*w^2 + 12*w - 1],\ [521, 521, 3/2*w^3 - 3/2*w^2 - 6*w + 1],\ [521, 521, -3/2*w^3 - 3/2*w^2 + 6*w + 1],\ [521, 521, 5/2*w^3 - 1/2*w^2 - 12*w - 1],\ [529, 23, -1/2*w^3 + 2*w - 5],\ [529, 23, 1/2*w^3 - 2*w - 5],\ [569, 569, 2*w^3 + 2*w^2 - 9*w - 5],\ [569, 569, -2*w^3 + w^2 + 12*w - 3],\ [569, 569, 2*w^3 + w^2 - 12*w - 3],\ [569, 569, -2*w^3 + 2*w^2 + 9*w - 5],\ [599, 599, 3/2*w^3 + 2*w^2 - 6*w - 3],\ [599, 599, w^3 - 5/2*w^2 - 5*w + 8],\ [599, 599, -w^3 - 5/2*w^2 + 5*w + 8],\ [599, 599, -3/2*w^3 + 2*w^2 + 6*w - 3],\ [601, 601, 5/2*w^3 - 3/2*w^2 - 12*w + 4],\ [601, 601, -3/2*w^3 - 3/2*w^2 + 4*w + 5],\ [601, 601, 3/2*w^3 - 3/2*w^2 - 4*w + 5],\ [601, 601, -5/2*w^3 - 3/2*w^2 + 12*w + 4],\ [631, 631, 2*w^3 - 1/2*w^2 - 9*w - 3],\ [631, 631, -3/2*w^3 + 1/2*w^2 + 5*w - 6],\ [631, 631, 3/2*w^3 + 1/2*w^2 - 5*w - 6],\ [631, 631, -2*w^3 - 1/2*w^2 + 9*w - 3],\ [641, 641, w^3 - 2*w^2 - 5*w + 3],\ [641, 641, 1/2*w^3 - 2*w^2 - w + 9],\ [641, 641, -1/2*w^3 - 2*w^2 + w + 9],\ [641, 641, -w^3 - 2*w^2 + 5*w + 3],\ [719, 719, -1/2*w^3 + 5/2*w^2 + 3*w - 9],\ [719, 719, -5/2*w^2 - w + 6],\ [719, 719, -5/2*w^2 + w + 6],\ [719, 719, 1/2*w^3 + 5/2*w^2 - 3*w - 9],\ [751, 751, -w^3 + w^2 + 5*w - 9],\ [751, 751, 1/2*w^3 - w^2 - w - 3],\ [751, 751, -1/2*w^3 - w^2 + w - 3],\ [751, 751, w^3 + w^2 - 5*w - 9],\ [761, 761, 3/2*w^3 + 3/2*w^2 - 8*w - 3],\ [761, 761, -1/2*w^3 + 3/2*w^2 + w - 9],\ [761, 761, 1/2*w^3 + 3/2*w^2 - w - 9],\ [761, 761, -3/2*w^3 + 3/2*w^2 + 8*w - 3],\ [769, 769, -1/2*w^3 + 1/2*w^2 - 6],\ [769, 769, -3/2*w^3 - 1/2*w^2 + 8*w - 3],\ [769, 769, 3/2*w^3 - 1/2*w^2 - 8*w - 3],\ [769, 769, 1/2*w^3 + 1/2*w^2 - 6],\ [809, 809, -3/2*w^3 + 2*w^2 + 9*w - 5],\ [809, 809, -2*w^3 - 3/2*w^2 + 11*w + 4],\ [809, 809, 2*w^3 - 3/2*w^2 - 11*w + 4],\ [809, 809, 3/2*w^3 + 2*w^2 - 9*w - 5],\ [839, 839, -1/2*w^3 + 5/2*w^2 + 2*w - 8],\ [839, 839, -1/2*w^3 + w^2 + 3*w - 9],\ [839, 839, 1/2*w^3 + w^2 - 3*w - 9],\ [839, 839, 1/2*w^3 + 5/2*w^2 - 2*w - 8],\ [841, 29, 5/2*w^2 - 9],\ [841, 29, -5/2*w^2 + 6],\ [881, 881, -w^3 + w^2 + 8*w - 5],\ [881, 881, -w^3 - w^2 + 8*w + 1],\ [881, 881, w^3 - w^2 - 8*w + 1],\ [881, 881, w^3 + w^2 - 8*w - 5],\ [911, 911, w^3 - 3/2*w^2 - 7*w + 1],\ [911, 911, -1/2*w^3 + 3/2*w^2 + 5*w - 8],\ [911, 911, 1/2*w^3 + 3/2*w^2 - 5*w - 8],\ [911, 911, -w^3 - 3/2*w^2 + 7*w + 1],\ [919, 919, -w^3 - w^2 + 2*w + 5],\ [919, 919, -2*w^3 + w^2 + 10*w - 1],\ [919, 919, 2*w^3 + w^2 - 10*w - 1],\ [919, 919, w^3 - w^2 - 2*w + 5],\ [929, 929, 2*w^3 - 12*w - 1],\ [929, 929, 4*w - 1],\ [929, 929, -4*w - 1],\ [929, 929, 2*w^3 - 12*w + 1],\ [991, 991, -2*w^3 + 1/2*w^2 + 10*w + 2],\ [991, 991, -2*w^2 + 2*w + 9],\ [991, 991, -2*w^2 - 2*w + 9],\ [991, 991, 2*w^3 + 1/2*w^2 - 10*w + 2]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [3, 1, -4, 3, 4, -1, -6, -1, 0, 5, 0, 0, -2, 8, -2, -1, -2, 8, -4, 16, -9, 6, -14, -4, 6, -4, 5, -10, 14, -16, -1, 14, 24, -1, 4, 9, -16, 14, 24, -11, -6, -16, -2, -12, -7, -2, -16, -26, -6, -11, -15, -10, -30, 20, -22, -2, -17, 18, -15, -20, 21, -9, -24, -9, 24, -6, -31, -6, -14, -9, -38, 27, -18, 12, -23, 12, 12, -18, 32, 12, -3, 7, -18, 7, -8, 32, -22, 23, -22, 18, -24, -9, 16, 6, 18, -17, -2, 18, 10, -30, 19, -6, -6, 9, 12, -33, 2, -3, 22, -8, 32, -18, 21, -4, 21, 6, -48, 2, 2, 2, 39, 24, 29, 44, -27, -47, -17, 48, 36, 26, 26, 31, -14, -4, 16, -9, 40, -10, -10, 50, 35, 0, -40, 10, 8, -42, 35, 0, 0, 15, -27, 38, 18, 43, 56, 31, -29, -49, -1, 34, -26, -26, 24, 29, -11, 4] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([71,71,1/2*w^3 - 1/2*w^2 - 2*w - 2])] = 1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]