  We study the zero mode solutions of a Dirac operator on a magnetized Riemann
surface of higher genus. In this paper, we define a Riemann surface of higher
genus as a quotient manifold of the Poincar$\acute{\text{e}}$ upper half-plane
by a congruence subgroup, especially $\Gamma_{0}(N)$. We present a method to
construct basis of cusp forms since the zero mode solutions should be cusp
forms. To confirm our method, we select a congruence subgroup of semiprime
level and show the demonstration to some lower weights. In addition, we discuss
Yukawa couplings and matrix regularization as applications.
