# SageMath code for working with modular form 810.4.e.be


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(810, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")

# select newform: 
traces = [4,4,0,-8,10,0,5,-32,0,40,51]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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