# SageMath code for working with modular form 27378.2.a.p


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
B = ModularForms(chi, 1).cuspidal_submodule().basis()
N = [B[i] for i in range(len(B))]

# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27378, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,1,0,1,0,0,-2,1,0,0,-3,0,0,-2,0,1,3,0,1,0,0,-3,6,0,-5,0,0,-2,
-6,0,4,1,0,3,0,0,4,1,0,0,9,0,-1,-3,0,6,-6,0,-3,-5,0,0,-12,0,0,-2,0,-6,
3,0,8,4,0,1,0,0,-5,3,0,0,-12,0,-11,4,0,1,6,0,-4,0,0,9,12,0,0,-1,0,-3,6,
0,0,6,0,-6,0,0,-5,-3,0,-5]
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