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

Magnetized Riemann Surface of Higher Genus and Eta Quotients of Semiprime Level