# SageMath code for working with modular form 10470.2.a.e


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,1,1,1,1,1,1,1,1,1,4,1,-3,1,1,1,3,1,-3,1,1,4,5,1,1,-3,1,1,6,
1,-5,1,4,3,1,1,6,-3,-3,1,-6,1,0,4,1,5,12,1,-6,1,3,-3,-4,1,4,1,-3,6,7,1,
4,-5,1,1,-3,4,-4,3,5,1,1,1,-14,6,1,-3,4,-3,-10,1,1,-6,3,1,3,0,6,4,15,1,
-3,5,-5,12,-3,1,2,-6,4,1]
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