Texture of Two Vanishing Subtraces in Neutrino Mass Matrix and Current Experimental Tests

We present a full phenomenological and analytical study for the neutrino mass matrix characterized by two vanishing $2\times 2$ subtraces. We update one past result in light of the recent experimental data. Out of the fifteen possible textures, we find seven cases can accommodate the experimental data instead of eight ones in the past study. We also introduce few symmetry realizations for viable and nonviable textures based on non-abelian ($A_4$ or $S_4$) flavor symmetry within type II seesaw scenario.