  We study fermion zero-mode wavefunctions on $T^4/Z_N$ orbifold with
background magnetic fluxes. The number of zero-modes is analyzed by use of
$Sp(4,\mathbb{Z})$ modular transformation. Conditions needed to realize three
generation models are clarified. We also study parity transformation in the
compact space which leads to better understanding of relationship between
positive and negative chirality wavefunctions.
