"""
  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([30, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((42, 7*a))

primes_array = [
(2,a),(3,a),(5,a),(11,a+5),(11,a+6),(13,a+3),(13,a+10),(17,a+2),(17,a+15),(23,a+4),(23,a+19),(29,a+12),(29,a+17),(a+1,),(a-1,),(37,a+9),(37,a+28),(43,a+20),(43,a+23),(47,a+8),(47,a+39),(7,),(59,a+18),(59,a+41),(67,a+29),(67,a+38)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, 1, 2, 4, 4, -6, -6, 2, 2, 8, 8, 2, 2, 0, 0, 10, 10, 4, 4, 0, 0, 1, -4, -4, -4, -4]
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((3, a))] = -1
AL_eigenvalues[ZF.ideal((7,))] = -1

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