# SageMath code for working with modular form 42978.2.a.r


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(42978, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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(42978, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,1,1,1,-4,1,-2,1,1,-4,-3,1,1,-2,-4,1,-7,1,-1,-4,-2,-3,-6,1,
11,1,1,-2,-1,-4,-3,1,-3,-7,8,1,-2,-1,1,-4,-8,-2,-1,-3,-4,-6,-12,1,-3,11,
-7,1,-11,1,12,-2,-1,-1,10,-4,7,-3,-2,1,-4,-3,-7,-7,-6,8,-3,1,-1,-2,11,
-1,6,1,-10,-4,1,-8,-6,-2,28,-1,-1,-3,0,-4,-2,-6,-3,-12,4,1,-2,-3,-3,11]
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