# SageMath code for working with modular form 98.8.c.d


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 8, names="a") 

# select newform: 
traces = [2,8,-12,-64,210,-192,0,-1024,2043]
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