"""
  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([37, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((14, 7*a + 7))

primes_array = [
(2,a+1),(3,),(19,a+1),(19,a+18),(23,a+3),(23,a+20),(5,),(31,a+5),(31,a+26),(a,),(a+2,),(a-2,),(43,a+7),(43,a+36),(7,),(a+4,),(a-4,),(59,a+9),(59,a+50),(a+6,),(a-6,),(79,a+11),(79,a+68),(a+8,),(a-8,),(103,a+13),(103,a+90),(11,),(131,a+15),(131,a+116),(a+10,),(a-10,),(-2*a+1,),(-2*a-1,),(-2*a+3,),(-2*a-3,),(163,a+17),(163,a+146),(167,a+56),(167,a+111),(13,),(-2*a+5,),(2*a+5,),(179,a+58),(179,a+121),(a+12,),(a-12,),(191,a+66),(191,a+125),(-2*a+7,),(2*a+7,),(199,a+19),(199,a+180),(227,a+72),(227,a+155),(-2*a+9,),(2*a+9,),(a+14,),(a-14,),(239,a+21),(239,a+218),(251,a+88),(251,a+163),(-2*a+11,),(2*a+11,),(283,a+23),(283,a+260),(17,),(a+16,),(a-16,),(311,a+98),(311,a+213),(-2*a+13,),(2*a+13,),(331,a+25),(331,a+306),(-3*a-2,),(3*a-2,),(347,a+122),(347,a+225),(-3*a+4,),(3*a+4,),(-2*a+15,),(2*a+15,),(383,a+27),(383,a+356),(-3*a-8,),(3*a-8,),(431,a+136),(431,a+295),(-3*a+10,),(3*a+10,),(439,a+29),(439,a+410),(463,a+185),(463,a+278),(467,a+94),(467,a+373),(479,a+168),(479,a+311)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [1, -2, -2, -2, 0, 0, -10, 4, 4, 2, 6, 6, -8, -8, 1, 6, 6, 6, 6, 2, 2, -8, -8, 0, 0, 4, 4, -22, -18, -18, 18, 18, -18, -18, -4, -4, 16, 16, 12, 12, -10, -12, -12, 12, 12, 20, 20, -24, -24, -18, -18, -20, -20, -18, -18, -4, -4, -6, -6, -24, -24, 18, 18, -12, -12, 22, 22, 2, 24, 24, 24, 24, 6, 6, -8, -8, 14, 14, 24, 24, -28, -28, 14, 14, -36, -36, 20, 20, -24, -24, -34, -34, -8, -8, -32, -32, 6, 6, 36, 36]
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))] = -1
AL_eigenvalues[ZF.ideal((7,))] = -1

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