"""
  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([105, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((35, a))

primes_array = [
(2,a+1),(3,a),(5,a),(7,a),(11,a+4),(11,a+7),(13,a+5),(13,a+8),(19,a+3),(19,a+16),(31,a+9),(31,a+22),(41,a+10),(41,a+31),(43,a+14),(43,a+29),(47,a+6),(47,a+41),(53,a+1),(53,a+52),(67,a+30),(67,a+37),(71,a+26),(71,a+45),(73,a+25),(73,a+48)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, 1, 1, -1, -3, -3, 5, 5, -2, -2, 4, 4, 12, 12, 10, 10, 9, 9, -12, -12, 4, 4, 0, 0, 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((5, a))] = -1
AL_eigenvalues[ZF.ideal((7, a))] = 1

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