"""
  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([5, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((38, 2*a + 18))

primes_array = [
(2,),(-a,),(a-1,),(-a-1,),(a-2,),(3,),(a+2,),(a-3,),(a+3,),(a-4,),(-2*a+1,),(-2*a+3,),(2*a+1,),(-3*a+1,),(3*a-2,),(a+6,),(a-7,),(a+7,),(a-8,),(-3*a+7,),(3*a+4,),(-2*a+9,),(2*a+7,),(-4*a-3,),(4*a-7,),(-5*a+6,),(5*a+1,),(a+11,),(a-12,),(5*a+2,),(5*a-7,),(-5*a+8,),(-5*a-3,),(-4*a-7,),(4*a-11,),(-2*a+13,),(2*a+11,),(13,),(-5*a+11,),(5*a+6,),(-4*a+13,),(4*a+9,),(-3*a-11,),(3*a-14,),(-5*a+13,),(-5*a-8,),(7*a-4,),(7*a-3,),(-7*a+1,),(7*a-6,),(-5*a-9,),(5*a-14,),(7*a+2,),(7*a-9,),(-6*a+13,),(6*a+7,),(a+16,),(a-17,),(-3*a-14,),(3*a-17,),(a+17,),(a-18,),(-8*a+1,),(8*a-7,),(a+18,),(a-19,),(-3*a+19,),(3*a+16,),(-8*a+11,),(-8*a-3,),(-5*a+18,),(-5*a-13,),(-6*a-11,),(6*a-17,),(7*a+9,),(7*a-16,),(-9*a+1,),(9*a-8,),(-2*a+21,),(2*a+19,),(-7*a+18,),(-7*a-11,),(9*a+4,),(9*a-13,),(-5*a+21,),(5*a+16,),(-3*a+22,),(3*a+19,),(a+21,),(a-22,),(10*a-7,),(10*a-3,),(-10*a+1,),(10*a-9,),(5*a+17,),(5*a-22,),(-2*a+23,),(2*a+21,),(-9*a-8,),(9*a-17,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, -4, -4, 3, 3, -5, 2, 2, 3, 3, -1, -1, -1, 4, 4, 8, 8, 2, 2, 9, 9, -6, -6, 2, 2, 12, 12, -17, -17, 0, 0, 0, 0, -2, -2, -16, -16, -25, 7, 7, 8, 8, -25, -25, -10, -10, -6, -6, 15, 15, 2, 2, 24, 24, 7, 7, 28, 28, -6, -6, 7, 7, 29, 29, -2, -2, 10, 10, 9, 9, -15, -15, 28, 28, -30, -30, 8, 8, 0, 0, -26, -26, -7, -7, -28, -28, 4, 4, -2, -2, -20, -20, -28, -28, 40, 40, 39, 39, 2, 2]
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((-2*a + 1,))] = 1

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