# SageMath code for working with modular form 12138.2.a.ck


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(12138, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [6,-6,6,6,-3,-6,-6,-6,6,3,-3,6,3,6,-3,6,0,-6,-6,-3,-6,3,6,-6,
-9,-3,6,-6,-6,3,9,-6,-3,0,3,6,-3,6,3,3,-12,6,12,-3,-3,-6,0,6,6,9,0,3,-24,
-6,-6,6,-6,6,6,-3,6,-9,-6,6,12,3,12,0,6,-3,3,-6,-3,3,-9,-6,3,-3,-21,-3,
6,12,0,-6,0,-12,-6,3,-24,3,-3,6,9,0,-12,-6,-36,-6,-3,-9]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)

# q-expansion: 
f.q_expansion() # note that sage often uses an isomorphic number field