# SageMath code for working with modular form 16731.2.a.m


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16731, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
B = ModularForms(chi, 1).cuspidal_submodule().basis()
N = [B[i] for i in range(len(B))]

# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(16731, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [1,1,0,-1,4,0,2,-3,0,4,1,0,0,2,0,-1,2,0,6,-4,0,1,4,0,11,0,0,-2,
-6,0,-4,5,0,2,8,0,6,6,0,-12,10,0,6,-1,0,4,8,0,-3,11,0,0,0,0,4,-6,0,-6,
-4,0,-6,-4,0,7,0,0,-8,-2,0,8,0,0,2,6,0,-6,2,0,-10,-4,0,10,-12,0,8,6,0,
-3,0,0,0,-4,0,8,24,0,-2,-3,0,-11]
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