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

NN = ZF.ideal((915, 5*a + 65))

primes_array = [
(a+1,),(2,),(-a-2,),(a-3,),(a+3,),(a-4,),(-2*a+5,),(2*a+3,),(5,),(a+5,),(a-6,),(-3*a+7,),(3*a+4,),(a+6,),(a-7,),(-4*a+9,),(4*a+5,),(-2*a+9,),(2*a+7,),(a+8,),(a-9,),(-3*a+10,),(3*a+7,),(-3*a-8,),(3*a-11,),(-2*a+11,),(2*a+9,),(5*a+7,),(5*a-12,),(11,),(-6*a+13,),(6*a+7,),(-3*a+13,),(3*a+10,),(-5*a-9,),(5*a-14,),(a+12,),(a-13,),(-3*a-11,),(3*a-14,),(-4*a-11,),(4*a-15,),(7*a+9,),(7*a-16,),(-2*a+15,),(2*a+13,),(a+14,),(a-15,),(-6*a-11,),(6*a-17,),(5*a+12,),(5*a-17,),(a+15,),(a-16,),(-9*a+19,),(9*a+10,),(7*a-19,),(7*a+12,),(-6*a+19,),(6*a+13,),(17,),(a+17,),(a-18,),(-3*a+19,),(3*a+16,),(-10*a+21,),(10*a+11,),(-8*a-13,),(-8*a+21,),(-3*a-17,),(3*a-20,),(9*a+13,),(9*a-22,),(-4*a+21,),(4*a+17,),(-7*a+22,),(7*a+15,),(-11*a+23,),(11*a+12,),(-8*a-15,),(8*a-23,),(a+20,),(a-21,),(11*a+13,),(11*a-24,),(-5*a+23,),(-5*a-18,),(7*a+17,),(7*a-24,),(a+21,),(a-22,),(-2*a+23,),(2*a+21,),(-7*a+25,),(-7*a-18,),(-9*a-17,),(9*a-26,),(23,),(-4*a+25,),(4*a+21,),(-13*a+27,),(13*a+14,),(-5*a+26,),(5*a+21,),(-8*a+27,),(-8*a-19,),(a+24,),(a-25,),(-3*a-23,),(3*a-26,),(-9*a+28,),(9*a+19,),(5*a+22,),(5*a-27,),(-14*a+29,),(14*a+15,),(-11*a-18,),(-11*a+29,),(9*a+20,),(9*a-29,),(-8*a-21,),(-8*a+29,),(-11*a-19,),(-11*a+30,),(-3*a+28,),(3*a+25,),(-13*a-18,),(13*a-31,),(12*a+19,),(-12*a+31,),(7*a+23,),(7*a-30,),(-10*a+31,),(10*a+21,),(a+27,),(a-28,),(15*a+17,),(15*a-32,),(-2*a+29,),(2*a+27,),(-6*a+31,),(6*a+25,),(-14*a+33,),(-14*a-19,),(-13*a+33,),(-13*a-20,),(29,),(-4*a-27,),(4*a-31,),(10*a+23,),(10*a-33,),(-3*a+31,),(3*a+28,),(13*a-34,),(-13*a-21,),(7*a-33,),(7*a+26,),(-17*a+35,),(17*a+18,),(-3*a-29,),(3*a-32,),(-7*a-27,),(7*a-34,),(-9*a-26,),(9*a-35,),(13*a-36,),(13*a+23,),(-8*a+35,),(-8*a-27,),(-11*a+36,),(-11*a-25,),(16*a+21,),(16*a-37,),(15*a+22,),(15*a-37,),(-6*a-29,),(6*a-35,),(-3*a+34,),(3*a+31,),(-12*a+37,),(12*a+25,),(17*a+21,),(17*a-38,),(-7*a+36,),(7*a+29,),(-9*a+37,),(9*a+28,),(a+33,),(a-34,),(-3*a-32,),(3*a-35,),(-16*a+39,),(16*a+23,),(-14*a-25,),(-14*a+39,),(19*a+21,),(19*a-40,),(-11*a+39,),(-11*a-28,),(-10*a-29,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, 3, -3, -3, -2, 4, 4, 7, 1, -6, 6, 8, 2, 4, 10, -1, -11, 12, -12, -5, -11, -9, 15, 2, -4, 2, -1, 2, 14, 12, 16, 10, 5, -16, 1, -23, -10, -13, -1, -10, 2, -7, -13, 14, 19, -20, -16, -19, 8, -1, 21, -27, -17, -2, -8, 25, -15, -24, -24, 6, 9, -2, 22, -34, -13, 12, 18, 28, 1, 7, 10, 15, -24, 4, 13, 4, 37, -2, -2, -7, -10, 19, -2, 37, -38, -20, 1, -5, -2, -42, 24, -13, 32, 37, -29, 1, 28, -28, -18, -30, -5, -20, -4, -22, 38, -22, 2, 14, -8, -5, 19, 7, -16, -28, 28, -26, -9, -12, 7, -14, -42, 21, 46, 49, 31, -8, -22, 23, 23, 14, -44, -11, -20, 22, -2, -11, -49, -16, 25, 19, -18, 24, 44, -10, 30, -12, 33, 42, 0, -44, -5, -42, -21, 14, -22, -3, -57, 46, -17, 15, -15, 14, -40, -4, -4, -12, -15, -10, -10, 7, -17, -27, 6, -5, 19, 12, 45, 2, -52, 22, -50, 17, 47, 49, 1, 36, 18, -44, -26, -10, -64, -53, -26, 9, 6, -68, -50, 39, 42, -18]
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,))] = 1
AL_eigenvalues[ZF.ideal((5,))] = -1
AL_eigenvalues[ZF.ideal((-4*a + 9,))] = 1

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