"""
  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((24, 24*a))

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 = [0, 4, 4, 1, -4, -4, -2, -6, -6, 4, 4, -6, 2, 2, -4, -4, -8, -8, 10, 10, 4, 4, 6, 6, -4, -4, 16, 16, -12, -12, -6, -6, 2, 2, -12, -12, -10, -10, 4, 4, -8, -8, -6, -6, -10, -10, 4, 4, -12, -12, -6, -6, 0, 0, 2, 2, 18, 18, -12, -12, 22, 22, 12, 12, 10, 10, -28, -28, 2, 2, -16, -16, -34, -34, 28, 28, -32, -32, -30, -30, -24, -24, -14, -14, 20, 20, 24, 24, 4, 4, 12, 12, -30, -30, -46, -46, -46, 36, 36, 10]
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((3,))] = -1

# EXAMPLE:
# pp = ZF.ideal(2).factor()[0][0]
# hecke_eigenvalues[pp]