"""
  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([150, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((18, 2*a + 10))

primes_array = [
(2,a),(2,a+1),(3,a),(3,a+2),(5,a),(5,a+4),(13,a+2),(13,a+10),(17,a+4),(17,a+12),(19,a+1),(19,a+17),(37,a+8),(37,a+28),(41,a+18),(41,a+22),(47,a+11),(47,a+35),(7,),(53,a+19),(53,a+33),(67,a+32),(67,a+34),(71,a+26),(71,a+44)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [-1, 1, -1, 0, 2, 1, -2, 1, 8, 1, 4, -5, -2, -8, -3, 12, 3, 3, -4, 6, 6, 4, -8, 12, 6]
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, a))] = 1
AL_eigenvalues[ZF.ideal((2, a + 1))] = -1
AL_eigenvalues[ZF.ideal((3, a + 2))] = 1

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