# SageMath code for working with modular form 15730.2.a.cl


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15730, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [5,-5,1,5,-5,-1,5,-5,8,5,0,1,5,-5,-1,5,1,-8,-5,-5,7,0,4,-1,5,
-5,7,5,1,1,3,-5,0,-1,-5,8,-5,5,1,5,16,-7,-2,0,-8,-4,6,1,0,-5,-31,5,-37,
-7,0,-5,-7,-1,18,-1,-19,-3,56,5,-5,0,-8,1,44,5,13,-8,-18,5,1,-5,0,-1,-18,
-5,65,-16,-4,7,-1,2,53,0,23,8,5,4,33,-6,5,-1,-2,0,0,5]
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