"""
  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([10, 0, 1])
F = NumberField(g, "a")
a = F.gen()
ZF = F.ring_of_integers()

NN = ZF.ideal((8, 4*a))

primes_array = [
(2,a),(5,a),(7,a+2),(7,a+5),(3,),(a+1,),(a-1,),(13,a+4),(13,a+9),(a+3,),(a-3,),(23,a+6),(23,a+17),(37,a+8),(37,a+29),(-2*a+1,),(2*a+1,),(47,a+15),(47,a+32),(53,a+19),(53,a+34),(a+7,),(a-7,),(-2*a+7,),(2*a+7,),(103,a+14),(103,a+89),(127,a+25),(127,a+102),(a+11,),(a-11,),(-3*a+7,),(3*a+7,),(157,a+33),(157,a+124),(167,a+18),(167,a+149),(173,a+63),(173,a+110),(a+13,),(a-13,),(197,a+37),(197,a+160),(-3*a-11,),(3*a-11,),(223,a+92),(223,a+131),(-4*a+9,),(4*a+9,),(-5*a+1,),(5*a+1,),(263,a+76),(263,a+187),(277,a+78),(277,a+199),(-4*a-11,),(4*a-11,),(17,),(293,a+24),(293,a+269),(317,a+47),(317,a+270),(-5*a-9,),(5*a-9,),(367,a+69),(367,a+298),(373,a+51),(373,a+322),(-3*a-17,),(3*a-17,),(383,a+119),(383,a+264),(397,a+28),(397,a+369),(-2*a+19,),(2*a+19,),(-6*a+7,),(6*a+7,),(-5*a+13,),(-5*a-13,),(-4*a+17,),(4*a+17,),(463,a+180),(463,a+283),(487,a+136),(487,a+351),(-7*a+1,),(7*a+1,),(7*a+3,),(7*a-3,),(503,a+222),(503,a+281),(-4*a-19,),(4*a-19,),(557,a+175),(557,a+382),(-2*a+23,),(2*a+23,),(7*a+9,),(7*a-9,)]
primes = [ZF.ideal(I) for I in primes_array]

heckePol = x
K = QQ
e = 1

hecke_eigenvalues_array = [0, -2, 0, 0, -6, 0, 0, 6, 6, 0, 0, 0, 0, -2, -2, 10, 10, 0, 0, 14, 14, 0, 0, 10, 10, 0, 0, 0, 0, 0, 0, 0, 0, 22, 22, 0, 0, -26, -26, 0, 0, -2, -2, 0, 0, 0, 0, -30, -30, 0, 0, 0, 0, -18, -18, 10, 10, -30, -34, -34, 22, 22, 0, 0, 0, 0, 14, 14, 0, 0, 0, 0, 38, 38, 2, 2, -6, -6, 0, 0, -14, -14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -22, -22, 38, 38, 26, 26, 0, 0]
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

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