# SageMath code for working with modular form 20339.2.a.p


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(20339, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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(20339, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [17,0,2,16,7,-3,8,6,17,-4,17,25,-3,23,1,10,3,-19,3,13,0,0,-11,
-3,20,7,11,15,-6,-9,5,-13,2,33,25,15,20,-21,-8,-4,8,19,0,16,-5,23,-18,
86,11,48,11,-22,-14,-24,7,24,4,7,-2,-9,27,5,15,50,6,-3,0,-15,-3,-6,57,
-90,-2,54,-12,13,8,48,2,4,1,4,-32,-4,44,0,10,6,79,-31,78,-2,44,-10,20,
-105,17,23,17,36]
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