# SageMath code for working with modular form 726.2.h.i


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(726, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [8,2,2,-2,0,-2,0,2,2]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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