# SageMath code for working with modular form 8281.2.a.bp


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8281, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [4,-1,-1,5,7,5,0,-6,7,11,-1,-12,0,0,3,19,4]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(17)] == traces)

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