/* 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([29, 11, -10, -2, 1]) F. = NumberField(g) ZF = F.ring_of_integers() NN = ZF.ideal([25, 5, -2*w^2 + 2*w + 11]) primes_array = [ [11, 11, -w - 1],\ [11, 11, w^2 - 5],\ [11, 11, -w^2 + 2*w + 4],\ [11, 11, w - 2],\ [16, 2, 2],\ [19, 19, w^2 - 2*w - 5],\ [19, 19, -w^2 + 6],\ [25, 5, -2*w^2 + 2*w + 11],\ [29, 29, w],\ [29, 29, 2*w^2 - w - 10],\ [29, 29, -2*w^2 + 3*w + 9],\ [29, 29, w - 1],\ [31, 31, w^3 - 6*w - 6],\ [31, 31, -w^3 + 3*w^2 + 3*w - 11],\ [41, 41, w^3 - 4*w^2 - 2*w + 16],\ [41, 41, w^3 - 5*w^2 - 2*w + 24],\ [59, 59, w^3 - w^2 - 5*w - 2],\ [59, 59, 2*w^2 - w - 13],\ [61, 61, w^3 - w^2 - 6*w + 3],\ [61, 61, -w^3 + 2*w^2 + 5*w - 3],\ [71, 71, 2*w^2 - w - 16],\ [71, 71, -w^3 + 3*w^2 + 4*w - 10],\ [71, 71, -w^3 + 7*w + 4],\ [71, 71, w^3 - 5*w^2 - 2*w + 23],\ [79, 79, -w^3 + 4*w^2 + 3*w - 16],\ [79, 79, w^3 + w^2 - 8*w - 10],\ [81, 3, -3],\ [131, 131, 4*w^2 - 5*w - 24],\ [131, 131, 4*w^2 - 3*w - 25],\ [139, 139, w^2 + w - 9],\ [139, 139, -w^3 + w^2 + 6*w - 5],\ [149, 149, w^3 - w^2 - 4*w + 2],\ [149, 149, w^3 - 2*w^2 - 3*w + 2],\ [151, 151, -w^3 + 7*w + 3],\ [151, 151, -w^3 + 3*w^2 + 4*w - 9],\ [179, 179, -w^3 - 2*w^2 + 10*w + 16],\ [179, 179, -w^3 + 3*w^2 + 3*w - 6],\ [179, 179, w^3 - 6*w - 1],\ [179, 179, w^3 - 5*w^2 - 3*w + 23],\ [191, 191, w^3 - 6*w^2 - w + 27],\ [191, 191, w^3 + 3*w^2 - 10*w - 21],\ [199, 199, -w^3 + 2*w^2 + 6*w - 4],\ [199, 199, -4*w^2 + 3*w + 22],\ [199, 199, 4*w^2 - 5*w - 21],\ [199, 199, 3*w^2 - 4*w - 12],\ [239, 239, -w^3 + w^2 + 4*w - 6],\ [239, 239, 2*w^3 - 5*w^2 - 9*w + 17],\ [239, 239, 2*w^3 - w^2 - 13*w - 5],\ [239, 239, w^3 - 8*w^2 + 2*w + 41],\ [241, 241, -w^3 + 5*w^2 + 4*w - 25],\ [241, 241, w^3 - 6*w - 8],\ [241, 241, -w^3 + 3*w^2 + 3*w - 13],\ [241, 241, w^3 - 5*w^2 + w + 19],\ [269, 269, w^2 - 2*w - 10],\ [269, 269, w^2 - 11],\ [271, 271, w^3 + 2*w^2 - 8*w - 18],\ [271, 271, 2*w^3 - 13*w - 10],\ [271, 271, 2*w^3 + w^2 - 15*w - 16],\ [271, 271, w^3 - 5*w^2 - w + 23],\ [289, 17, 2*w^2 - 11],\ [289, 17, -2*w^2 + 4*w + 9],\ [311, 311, w^3 - 4*w^2 - 3*w + 10],\ [311, 311, w^3 - 7*w^2 - w + 34],\ [331, 331, w^3 - w^2 - 7*w + 4],\ [331, 331, w^3 - 2*w^2 - 6*w + 3],\ [349, 349, w^3 + w^2 - 6*w - 12],\ [349, 349, -w^3 + 4*w^2 + w - 16],\ [361, 19, 4*w^2 - 4*w - 21],\ [379, 379, w^3 - 3*w^2 - 3*w + 15],\ [379, 379, 2*w^3 - 2*w^2 - 12*w + 1],\ [379, 379, -2*w^3 + 4*w^2 + 10*w - 11],\ [379, 379, w^3 - 6*w - 10],\ [401, 401, -2*w^3 + 7*w^2 + 8*w - 30],\ [401, 401, -w^3 + 2*w^2 + 6*w - 2],\ [419, 419, 5*w^2 - 4*w - 26],\ [419, 419, 5*w^2 - 6*w - 25],\ [421, 421, 3*w^2 - w - 20],\ [421, 421, -2*w^3 + 2*w^2 + 10*w + 3],\ [431, 431, w^2 - 3*w - 5],\ [431, 431, w^2 + w - 7],\ [449, 449, 2*w^3 - 13*w - 7],\ [449, 449, -2*w^3 + 6*w^2 + 7*w - 18],\ [461, 461, w^3 - w^2 - 8*w + 3],\ [461, 461, -w^3 + 2*w^2 + 7*w - 5],\ [491, 491, w^3 - 3*w^2 - 6*w + 15],\ [491, 491, w^3 - 9*w - 7],\ [499, 499, 4*w^2 - 6*w - 23],\ [499, 499, -4*w^2 + 2*w + 25],\ [509, 509, 2*w^3 - 3*w^2 - 11*w + 6],\ [521, 521, -w^3 + 3*w^2 + 2*w - 12],\ [521, 521, -w^3 + 4*w^2 + 2*w - 19],\ [529, 23, w^3 - 7*w^2 - w + 35],\ [529, 23, -w^3 + 3*w^2 + 4*w - 5],\ [541, 541, 2*w^3 - w^2 - 12*w - 5],\ [541, 541, w^3 - 2*w^2 - 7*w + 9],\ [569, 569, w^3 - 8*w - 2],\ [569, 569, -w^3 + 3*w^2 + 5*w - 9],\ [599, 599, -w^3 - 4*w^2 + 10*w + 25],\ [599, 599, -w^3 + 7*w^2 - 36],\ [601, 601, 5*w^2 - 6*w - 26],\ [601, 601, -2*w^3 + 8*w^2 + 6*w - 33],\ [601, 601, -2*w^3 - 2*w^2 + 16*w + 21],\ [601, 601, 5*w^2 - 4*w - 27],\ [619, 619, w^3 + 4*w^2 - 11*w - 26],\ [619, 619, w^3 - 3*w^2 - 5*w + 18],\ [641, 641, -w^3 + 3*w^2 + 6*w - 14],\ [641, 641, -w^3 + 9*w + 6],\ [659, 659, -w^3 - 4*w^2 + 10*w + 28],\ [659, 659, -w^3 + 6*w^2 - w - 27],\ [659, 659, -w^3 - 3*w^2 + 8*w + 23],\ [659, 659, -w^3 + 7*w^2 - w - 33],\ [691, 691, w^3 - w^2 - 8*w + 2],\ [691, 691, 2*w^3 - 2*w^2 - 11*w + 1],\ [701, 701, -w^3 - w^2 + 7*w + 15],\ [701, 701, -w^3 + 4*w^2 + 2*w - 20],\ [709, 709, -2*w^3 - w^2 + 15*w + 15],\ [709, 709, 2*w^3 - 7*w^2 - 7*w + 27],\ [719, 719, -w^3 - 4*w^2 + 13*w + 26],\ [719, 719, w^3 - 7*w^2 - 2*w + 34],\ [739, 739, 2*w^3 + 2*w^2 - 15*w - 24],\ [739, 739, -2*w^3 + 8*w^2 + 5*w - 35],\ [751, 751, -w^3 - 3*w^2 + 9*w + 25],\ [751, 751, -w^3 + 6*w^2 - 30],\ [761, 761, 3*w^3 - 2*w^2 - 16*w - 8],\ [761, 761, -3*w^3 + 7*w^2 + 11*w - 23],\ [769, 769, -2*w^3 + 4*w^2 + 11*w - 10],\ [769, 769, w^3 + 2*w^2 - 9*w - 12],\ [809, 809, -3*w^3 + 3*w^2 + 16*w + 4],\ [809, 809, w^3 + 5*w^2 - 12*w - 30],\ [811, 811, -w^3 - 4*w^2 + 10*w + 27],\ [811, 811, -2*w^3 + 5*w^2 + 9*w - 14],\ [811, 811, -2*w^3 + w^2 + 13*w + 2],\ [811, 811, -w^3 + 7*w^2 - w - 32],\ [821, 821, 2*w^3 - 8*w^2 - 7*w + 35],\ [821, 821, -2*w^3 - 2*w^2 + 17*w + 22],\ [829, 829, -3*w^3 + 20*w + 13],\ [829, 829, -w^3 + 7*w^2 - w - 36],\ [829, 829, w^3 + 4*w^2 - 10*w - 31],\ [829, 829, 2*w^3 - 3*w^2 - 11*w + 14],\ [859, 859, -w^3 + 7*w^2 - 3*w - 31],\ [859, 859, 7*w^2 - 9*w - 39],\ [859, 859, 7*w^2 - 5*w - 41],\ [859, 859, 3*w^3 - 4*w^2 - 17*w + 2],\ [929, 929, w^3 + 5*w^2 - 14*w - 31],\ [929, 929, -2*w^3 + 4*w^2 + 10*w - 5],\ [929, 929, w^3 - 9*w^2 + 4*w + 44],\ [929, 929, -w^3 + 8*w^2 + w - 39],\ [941, 941, -w^3 + 7*w^2 - 34],\ [941, 941, w^3 + 4*w^2 - 11*w - 28],\ [961, 31, -5*w^2 + 5*w + 28],\ [971, 971, -3*w^3 + w^2 + 19*w + 14],\ [971, 971, -3*w^3 + 8*w^2 + 12*w - 31],\ [991, 991, -w^3 - 5*w^2 + 11*w + 35],\ [991, 991, w^3 - 8*w^2 + 2*w + 40]] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-4, -5, 3, 0, -4, 2, 8, 1, -4, 8, -8, -2, -5, -1, 3, -5, -8, 10, 10, -2, -8, -11, 9, -8, -8, 12, 5, -7, 1, 14, 12, -14, 10, 19, -17, 6, -24, 18, -6, -3, -23, 16, -10, -14, 22, -8, 28, 6, -6, -18, -25, -21, -10, 10, 6, 19, 25, -7, 3, -6, -20, 3, -21, -4, -20, 26, -16, -30, -32, 4, -26, -6, -33, -9, -12, 30, -23, 5, -11, 33, 30, 4, 2, 10, -27, 1, -30, 6, 10, -39, 13, 36, -40, 7, 23, 20, -8, -14, 0, -5, -27, -19, 35, 22, 24, 23, -33, -24, 10, 10, 20, -21, 7, 29, 17, 32, 48, -14, -22, -26, 18, -45, 15, -6, 22, -40, -26, 30, 6, -5, -16, -20, -33, 11, -13, 50, -14, 30, 4, -48, 40, -40, -36, 20, -48, -34, -48, 39, -45, -54, -7, -55, -7, -35] hecke_eigenvalues = {} for i in range(len(hecke_eigenvalues_array)): hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i] AL_eigenvalues = {} AL_eigenvalues[ZF.ideal([25, 5, -2*w^2 + 2*w + 11])] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]