"""
  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([10, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((15, 5*a + 5))

primes_array = [
(2,a),(2,a+1),(3,a+1),(5,a),(5,a+4),(11,a+3),(11,a+7),(13,a+6),(41,a+8),(41,a+32),(-2*a+3,),(2*a+1,),(47,a+16),(47,a+30),(7,),(59,a+21),(59,a+37),(61,a+24),(61,a+36),(71,a+11),(71,a+59),(79,a+17),(79,a+61),(83,a+12),(83,a+70),(89,a+26),(89,a+62),(-2*a+9,),(2*a+7,),(127,a+35),(127,a+91),(137,a+28),(137,a+108),(-2*a+11,),(2*a+9,),(149,a+54),(149,a+94),(-4*a+1,),(4*a-3,),(167,a+31),(167,a+135),(-4*a-3,),(4*a-7,),(197,a+71),(197,a+125),(199,a+44),(199,a+154),(211,a+79),(211,a+131),(227,a+42),(227,a+184),(239,a+102),(239,a+136),(-4*a+13,),(4*a+9,),(281,a+23),(281,a+257),(283,a+33),(283,a+249),(17,),(293,a+113),(293,a+179),(313,a+141),(313,a+171),(317,a+43),(317,a+273),(337,a+100),(337,a+236),(353,a+145),(353,a+207),(359,a+53),(359,a+305),(19,),(-6*a+7,),(6*a+1,),(373,a+38),(373,a+334),(383,a+27),(383,a+355),(401,a+89),(401,a+311),(431,a+192),(431,a+238),(433,a+41),(433,a+391),(-2*a+21,),(2*a+19,),(449,a+189),(449,a+259),(461,a+52),(461,a+408),(479,a+169),(479,a+309),(509,a+159),(509,a+349),(-2*a+23,),(2*a+21,),(23,),(-6*a-11,),(6*a-17,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, -1, -1, 1, 1, -4, -4, -2, 10, 10, 4, 4, 8, 8, -14, -4, -4, -2, -2, -8, -8, 0, 0, 12, 12, -6, -6, -16, -16, -8, -8, -6, -6, -4, -4, 22, 22, 14, 14, 0, 0, -10, -10, 6, 6, -8, -8, 20, 20, -20, -20, -16, -16, 6, 6, -6, -6, -12, -12, -30, 6, 6, 26, 26, -2, -2, -14, -14, 18, 18, -24, -24, -22, -24, -24, -26, -26, -24, -24, 18, 18, 0, 0, -14, -14, 40, 40, 2, 2, -18, -18, 0, 0, -34, -34, 4, 4, -46, -20, -20]
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))] = 1
AL_eigenvalues[ZF.ideal((5, a))] = -1
AL_eigenvalues[ZF.ideal((5, a + 4))] = -1

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