# SageMath code for working with modular form 17689.2.a.cd


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(17689, 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(17689, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a") 

# select newform: 
traces = [12,-1,3,11,0,-6,0,-9,9,16,1,-2,6,0,9,9,8,-5,0,0,0,2,9,-8,14,
1,9,0,2,9,11,-24,3,6,0,7,14,0,10,42,20,0,-2,-2,-12,6,0,39,0,11,-21,11,
-7,-43,9,0,0,-35,42,6,6,-19,0,-1,27,3,14,51,17,0,-1,-18,-21,25,31,0,0,
-57,5,13,-28,-12,-5,0,27,-18,53,36,-1,27,0,72,-34,12,0,-94,31,0,-43,-7]
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