# SageMath code for working with modular form 2601.2.a.bf


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2601, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")

# select newform: 
traces = [4,2,0,6,6,0,-4,6,0,12,6,0,2,4,0,6,0,0,10,16,0,-4,-6,0,2,20,0,
-24,16,0,-4,14,0,0,-4,0,-12,12,0,8,-14,0,14,-16,0,12,-4,0,0,30,0,-8,20,
0,2,-16,0,-8,24,0,-12,16,0,-2,14,0,4,0,0,-4,4,0,-20]
f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(73)] == traces)

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