""" This code can be loaded, or copied and paste using cpaste, into Sage. It will load the data associated to the BMF, including the field, level, and Hecke and Atkin-Lehner eigenvalue data (if known). """ P = PolynomialRing(QQ, "x") x = P.gen() g = P([13, 0, 1]) F = NumberField(g, "a") a = F.gen() ZF = F.ring_of_integers() NN = ZF.ideal((238, a + 223)) primes_array = [ (2,a+1),(7,a+1),(7,a+6),(3,),(11,a+3),(11,a+8),(a,),(a+2,),(a-2,),(19,a+5),(19,a+14),(5,),(a+4,),(a-4,),(31,a+7),(31,a+24),(47,a+9),(47,a+38),(-2*a+1,),(-2*a-1,),(59,a+20),(59,a+39),(-2*a+3,),(2*a+3,),(67,a+11),(67,a+56),(71,a+22),(71,a+49),(83,a+30),(83,a+53),(-2*a+7,),(2*a+7,),(a+10,),(a-10,),(151,a+17),(151,a+134),(a+12,),(a-12,),(163,a+65),(163,a+98),(167,a+34),(167,a+133),(-2*a+11,),(2*a+11,),(-3*a-8,),(3*a-8,),(223,a+87),(223,a+136),(227,a+21),(227,a+206),(-4*a+5,),(4*a+5,),(239,a+86),(239,a+153),(-4*a-7,),(4*a-7,),(a+16,),(a-16,),(271,a+23),(271,a+248),(-2*a+15,),(2*a+15,),(307,a+58),(307,a+249),(-3*a-14,),(3*a-14,),(331,a+48),(331,a+283),(a+18,),(a-18,),(359,a+50),(359,a+309),(-3*a+16,),(3*a+16,),(379,a+164),(379,a+215),(383,a+149),(383,a+234),(-5*a+8,),(-5*a-8,),(431,a+121),(431,a+310),(-4*a-15,),(4*a-15,),(463,a+196),(463,a+267),(479,a+150),(479,a+329),(487,a+31),(487,a+456),(499,a+74),(499,a+425),(-5*a-14,),(5*a-14,),(23,),(-4*a-19,),(4*a-19,),(587,a+64),(587,a+523),(-3*a+22,)] primes = [ZF.ideal(I) for I in primes_array] heckePol = x K = QQ e = 1 hecke_eigenvalues_array = [-1, 0, -1, 2, 4, 0, -2, 1, 2, 8, -8, 2, 6, -6, 0, 8, -8, 0, 2, 10, -8, 0, 2, 14, 4, 12, -8, -8, 12, -12, 10, 18, 2, 18, 8, 0, 2, -14, 8, -4, -8, -24, 22, 2, -2, -6, -16, -8, -12, -8, -6, -6, 0, 16, 18, 2, -6, -2, 8, 32, 6, 2, -16, 0, 26, -14, 20, 12, 18, 26, -32, -8, -22, 34, 16, -28, 24, -8, 38, -10, -16, -24, -14, 10, 16, 32, 32, 16, 16, -8, -40, 20, -6, -30, -6, -22, -6, 24, 8, -30] 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, a + 1))] = 1 AL_eigenvalues[ZF.ideal((7, a + 6))] = 1 AL_eigenvalues[ZF.ideal((a + 2,))] = -1 # EXAMPLE: # pp = ZF.ideal(2).factor()[0][0] # hecke_eigenvalues[pp]