"""
  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([3, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((8214, 6*a + 3912))

primes_array = [
(-a,),(a-1,),(2,),(-a-1,),(a-2,),(-2*a+1,),(a+4,),(a-5,),(-3*a+4,),(3*a+1,),(-3*a-2,),(3*a-5,),(-2*a+7,),(2*a+5,),(7,),(-4*a+5,),(4*a+1,),(a+7,),(a-8,),(-3*a-5,),(3*a-8,),(-5*a+1,),(5*a-4,),(5*a+2,),(5*a-7,),(-3*a+10,),(3*a+7,),(-6*a+1,),(6*a-5,),(a+10,),(a-11,),(7*a-5,),(7*a-2,),(-3*a+13,),(3*a+10,),(-6*a-5,),(6*a-11,),(13,),(-5*a+13,),(-5*a-8,),(-3*a-11,),(3*a-14,),(-7*a+11,),(-7*a-4,),(-6*a+13,),(6*a+7,),(9*a-5,),(9*a-4,),(9*a-7,),(9*a-2,),(-5*a+16,),(5*a+11,),(-8*a-5,),(-8*a+13,),(-4*a+17,),(4*a+13,),(17,),(-10*a+11,),(10*a+1,),(-9*a+14,),(-9*a-5,),(7*a+10,),(7*a-17,),(-3*a+19,),(3*a+16,),(-11*a+1,),(11*a-10,),(19,),(-3*a-17,),(3*a-20,),(-9*a-8,),(9*a-17,),(a+19,),(a-20,),(11*a+2,),(11*a-13,),(-12*a+5,),(12*a-7,),(-8*a+19,),(-8*a-11,),(10*a-17,),(10*a+7,),(-12*a+1,),(12*a-11,),(-9*a+19,),(9*a+10,),(11*a+5,),(11*a-16,),(5*a+17,),(5*a-22,),(9*a+11,),(9*a-20,),(-13*a+8,),(13*a-5,),(-3*a-20,),(3*a-23,),(-6*a-17,),(6*a-23,),(a+22,),(a-23,),(-13*a+14,),(13*a+1,),(-3*a+25,),(3*a+22,),(-2*a+25,),(2*a+23,),(10*a+13,),(10*a-23,),(-8*a+25,),(8*a+17,),(15*a-8,),(15*a-7,),(-15*a+4,),(-15*a+11,),(7*a-26,),(7*a+19,),(9*a-25,),(9*a+16,),(-13*a+20,),(-13*a-7,),(a+25,),(a-26,),(-15*a+1,),(15*a-14,),(-14*a+19,),(-14*a-5,),(-15*a+16,),(15*a+1,),(15*a+2,),(15*a-17,),(-5*a+28,),(-5*a-23,),(-3*a+28,),(3*a+25,),(-15*a+19,),(-15*a-4,),(-12*a+25,),(12*a+13,),(-4*a+29,),(4*a+25,),(-17*a+7,),(17*a-10,),(9*a+20,),(9*a-29,),(15*a+7,),(15*a-22,),(-11*a+28,),(-11*a-17,),(29,),(-15*a+23,),(-15*a-8,),(-14*a-11,),(-14*a+25,),(-5*a+31,),(5*a+26,),(-6*a+31,),(6*a+25,),(-18*a+13,),(18*a-5,),(-2*a+31,),(2*a+29,),(-16*a+23,),(16*a+7,),(-7*a+32,),(-7*a-25,),(13*a+16,),(13*a-29,),(-17*a+22,),(17*a+5,),(11*a-31,),(11*a+20,),(-18*a+19,),(18*a+1,),(-19*a+5,),(-19*a+14,),(12*a+19,),(-12*a+31,),(15*a-28,),(15*a+13,),(19*a-17,),(19*a-2,),(-5*a-29,),(5*a-34,),(-18*a-5,),(18*a-23,),(9*a-34,),(9*a+25,),(-19*a+20,),(19*a+1,),(-20*a+7,),(-20*a+13,),(-6*a-29,),(6*a-35,),(-9*a-26,),(9*a-35,),(-15*a+31,),(15*a+16,),(-20*a+1,),(20*a-19,),(a+34,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, -1, 1, -1, -3, 0, -6, -4, -5, -7, -3, 0, 12, -8, -6, -4, -9, 0, -9, -2, 7, 0, -5, 0, 6, -13, 2, -11, 11, -1, -9, -3, 12, 17, 2, -6, -24, -20, 10, -1, 0, 0, -8, -10, -25, 16, -11, -16, 4, 4, -10, -23, -2, -17, 16, 21, -15, -20, 33, -24, -9, 12, -17, -17, -20, 16, 6, -5, -2, -7, -36, -21, -16, -6, -4, -30, -32, -8, -22, -10, 36, 1, -3, 30, 26, -14, -26, -24, -10, 39, -34, -14, 12, -23, -8, -7, 5, 9, 30, 40, -3, 18, 28, -7, 18, -17, 40, 30, -12, -33, 40, 35, 33, 15, -18, -23, -4, 36, -38, -17, 34, -49, 35, 38, -24, 29, -22, 37, 31, -20, 0, 5, -28, -18, -30, -40, 23, -32, -31, 14, 3, 2, -31, -26, -10, -46, 54, -34, -15, 40, -4, -6, 24, 30, 0, 4, 41, 28, -13, 10, 13, -15, 30, 8, 7, -57, 33, 28, -12, 9, 31, 40, 22, -14, -36, 18, -30, -41, 56, -30, -6, -43, 18, -17, -33, -39, 6, 21, -11, -60, 15, -6, -24, -11, 34, 0, -12, 15, -10, 26]
hecke_eigenvalues = {}
for i in range(len(hecke_eigenvalues_array)):
    hecke_eigenvalues[primes[i]] = hecke_eigenvalues_array[i]

AL_eigenvalues = {}
AL_eigenvalues[ZF.ideal((-a,))] = -1
AL_eigenvalues[ZF.ideal((a - 1,))] = 1
AL_eigenvalues[ZF.ideal((2,))] = -1
AL_eigenvalues[ZF.ideal((3*a - 5,))] = -1

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