  We study the phenomenological implications of the modular symmetry $\Gamma(3)
\simeq A_4$ of lepton flavors facing recent experimental data of neutrino
oscillations. The mass matrices of neutrinos and charged leptons are
essentially given by fixing the expectation value of modulus $\tau$, which is
the only source of modular invariance breaking. We introduce no flavons in
contrast with the conventional flavor models with $A_4$ symmetry. We classify
our neutrino models along with the type I seesaw model, the Weinberg operator
model and the Dirac neutrino model. In the normal hierarchy of neutrino masses,
the seesaw model is available by taking account of recent experimental data of
neutrino oscillations and the cosmological bound of sum of neutrino masses. The
predicted $\sin^2\theta_{23}$ is restricted to be larger than $0.54$ and
$\delta_{CP}=\pm (50^{\circ}\mbox{--}180^{\circ})$. Since the correlation of
$\sin^2\theta_{23}$ and $\delta_{CP}$ is sharp, the prediction is testable in
the future. It is remarkable that the effective mass $m_{ee}$ of the
neutrinoless double beta decay is around $22$\,meV while the sum of neutrino
masses is predicted to be $145$\,meV. On the other hand, for the inverted
hierarchy of neutrino masses, only the Dirac neutrino model is consistent with
the experimental data.
