"""
  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([9, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((24, 24*a))

primes_array = [
(3,a),(3,a+2),(2,),(5,a+2),(7,a+3),(a+1,),(a-2,),(13,a+5),(13,a+7),(17,a+6),(17,a+10),(a+4,),(a-5,),(47,a+11),(47,a+35),(-2*a+7,),(2*a+5,),(73,a+14),(73,a+58),(-3*a+1,),(3*a-2,),(83,a+15),(83,a+67),(97,a+40),(97,a+56),(103,a+22),(103,a+80),(-3*a+7,),(3*a+4,),(-4*a+5,),(4*a+1,),(-3*a+10,),(3*a+7,),(157,a+21),(157,a+135),(167,a+46),(167,a+120),(173,a+75),(173,a+97),(-2*a+13,),(2*a+11,),(a+13,),(a-14,),(-3*a+13,),(3*a+10,),(223,a+61),(223,a+161),(227,a+86),(227,a+140),(5*a+2,),(5*a-7,),(257,a+107),(257,a+149),(a+16,),(a-17,),(283,a+37),(283,a+245),(293,a+29),(293,a+263),(307,a+117),(307,a+189),(313,a+30),(313,a+282),(-6*a+7,),(6*a+1,),(353,a+160),(353,a+192),(-2*a+19,),(2*a+17,),(19,),(367,a+99),(367,a+267),(-6*a-5,),(6*a-11,),(383,a+70),(383,a+312),(a+19,),(a-20,),(397,a+181),(397,a+215),(-5*a+16,),(5*a+11,),(-3*a-17,),(3*a-20,),(7*a-5,),(7*a-2,),(433,a+119),(433,a+313),(-7*a+8,),(7*a+1,),(467,a+171),(467,a+295),(-5*a-14,),(5*a-19,),(-3*a+22,),(3*a+19,),(503,a+116),(503,a+386),(523,a+39),(523,a+483)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, -1, 0, -2, 0, 4, 4, -2, -2, 2, 2, 6, 6, 0, 0, 8, 8, 10, 10, -8, -8, -4, -4, 2, 2, 16, 16, -2, -2, 14, 14, -16, -16, -2, -2, 24, 24, 6, 6, 12, 12, 0, 0, -20, -20, -8, -8, 12, 12, -16, -16, 2, 2, 26, 26, -28, -28, -18, -18, 12, 12, -6, -6, 20, 20, 2, 2, -24, -24, -22, -8, -8, 20, 20, 0, 0, -2, -2, 14, 14, -30, -30, -10, -10, 32, 32, -14, -14, -14, -14, -36, -36, -12, -12, 12, 12, 24, 24, 4, 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((3, a))] = 1
AL_eigenvalues[ZF.ideal((3, a + 2))] = 1
AL_eigenvalues[ZF.ideal((2,))] = -1

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