"""
  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([28, -1, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((48, 16*a + 16))

primes_array = [
(2,a),(2,a+1),(3,a+1),(5,a+1),(5,a+3),(7,a),(7,a+6),(17,a+2),(17,a+14),(23,a+10),(23,a+12),(29,a+5),(29,a+23),(37,a+18),(59,a+9),(59,a+49),(67,a+15),(67,a+51),(73,a+26),(73,a+46),(89,a+22),(89,a+66),(113,a+25),(113,a+87),(11,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, 0, -1, -2, 2, 3, 3, 3, -3, -1, 1, 6, -6, -12, -6, 6, 8, 8, 1, 1, 9, -9, 14, -14, -13]
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 + 1))] = 1

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