# SageMath code for working with modular form 22743.2.a.b


# Compute space of new eigenforms: 
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22743, 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(22743, 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,-3,0,1,3,0,3,1,0,6,-1,0,-1,-1,0,0,3,0,-1,0,0,4,-6,
0,-1,-6,0,0,-5,0,1,-3,0,7,0,0,-9,-7,0,8,-1,0,0,-2,0,1,-4,0,-6,6,0,-3,3,
0,6,14,0,4,0,0,7,-18,0,2,1,0,3,-8,0,10,-7,0,0,1,0,0,3,0,7,12,0,3,-8,0,
3,1,0,6,0,0,2,0,0,-8,-1,0,-4]
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