  We present a comprehensive analysis of neutrino mass and lepton mixing in
theories with $A_4$ modular symmetry, where the only flavon field is the single
modulus field $\tau$, and all masses and Yukawa couplings are modular forms.
Similar to previous analyses, we discuss all the simplest neutrino sectors
arising from both the Weinberg operator and the type I seesaw mechanism, with
lepton doublets and right-handed neutrinos assumed to be triplets of $A_4$.
Unlike previous analyses, we allow right-handed charged leptons to transform as
all combinations of $\mathbf{1}$, $\mathbf{1}'$ and $\mathbf{1}''$
representations of $A_4$, using the simplest different modular weights to break
the degeneracy, leading to ten different charged lepton Yukawa matrices,
instead of the usual one. This implies ten different Weinberg models and thirty
different type I seesaw models, which we analyse in detail. We find that
fourteen models for both NO and IO neutrino mass ordering can accommodate the
data, as compared to one in previous analyses, providing many new
possibilities.
