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


# 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,-1,1,1,7,-1,5,1,1,4,-3,-1,1,
3,1,1,2,-1,-1,-1,-4,-7,1,1,-10,-5,-3,-1,2,-1,-8,-4,1,3,-12,1,-6,-1,7,-3,
-8,-1,-4,-1,5,-2,-9,1,0,1,1,1,-3,4,-4,7,-3,-1,5,-1,-2,10,1,5,-4,3,-10,
1,1,-2,7,1,7,8,2,4,-9,-1,-3,-3,-1,12,5,-1,-6,6,-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