  We study $T^2/Z_N$ orbifold models with magnetic fluxes. We propose a
systematic way to analyze the number of zero-modes and their wavefunctions by
use of modular transformation. Our results are consistent with the previous
results, and our approach is more direct and analytical than the previous ones.
The index theorem implies that the zero-mode number of the Dirac operator on
$T^2$ is equal to the index $M$, which corresponds to the magnetic flux in a
certain unit. Our results show that the zero-mode number of the Dirac operator
on $T^2/Z_N$ is equal to $\lfloor M/N \rfloor +1$ except one case on the
$T^2/Z_3$ orbifold.
