# SageMath code for working with modular form 825.2.n.c


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [4,1,-1,-9,0,1,-1,-13,-1,0,-11]
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