"""
  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([17, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((136, 8*a + 128))

primes_array = [
(2,),(3,),(-a,),(a-1,),(a+1,),(a-2,),(a+2,),(a-3,),(5,),(a+3,),(a-4,),(a+4,),(a-5,),(a+5,),(a-6,),(7,),(a+6,),(a-7,),(-2*a+1,),(-2*a+3,),(2*a+1,),(a+7,),(a-8,),(-2*a+5,),(2*a+3,),(a+8,),(a-9,),(-2*a+7,),(2*a+5,),(a+9,),(a-10,),(11,),(a+10,),(a-11,),(-2*a+9,),(2*a+7,),(a+11,),(a-12,),(-3*a+1,),(3*a-2,),(-3*a+4,),(3*a+1,),(-3*a-2,),(3*a-5,),(-2*a+11,),(2*a+9,),(13,),(a+12,),(a-13,),(-3*a+7,),(3*a+4,),(-3*a-5,),(3*a-8,),(a+13,),(a-14,),(-2*a+13,),(2*a+11,),(-3*a+10,),(3*a+7,),(a+14,),(a-15,),(-3*a-8,),(3*a-11,),(a+15,),(a-16,),(-2*a+15,),(2*a+13,),(-4*a+1,),(4*a-3,),(-4*a+5,),(4*a+1,),(-3*a+13,),(3*a+10,),(-4*a-3,),(4*a-7,),(-3*a-11,),(3*a-14,),(-4*a+9,),(4*a+5,),(-4*a-7,),(4*a-11,),(a+18,),(a-19,),(-4*a+13,),(4*a+9,),(a+19,),(a-20,),(-5*a+3,),(-5*a+2,),(-5*a+1,),(5*a-4,),(-5*a+6,),(5*a+1,),(5*a+2,),(5*a-7,),(-5*a+8,),(-5*a-3,),(-3*a+19,),(3*a+16,),(-5*a-4,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, 2, 2, 1, 0, -4, 6, 4, 2, -2, 6, -10, 10, -6, -2, -6, -10, 6, -4, 0, 6, -2, 10, -6, -14, -6, -2, 14, -6, -10, -8, -6, 2, -6, 14, 8, -2, 14, -12, -16, -14, -14, 18, -16, 12, 18, 6, -18, 6, -22, -18, -14, -6, 14, 0, -10, -28, 2, -14, -8, -22, -22, -10, -30, 6, -16, -4, -10, -18, 10, -10, -2, 20, -10, 14, -14, -10, -10, -18, -18, -2, 12, 16, 18, 6, -2, -38, -24, -22, -22, 6, -16, 18, 26, 28, -6, 18, 22, -22, 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,))] = -1
AL_eigenvalues[ZF.ideal((a - 1,))] = -1

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