Modüler formaların Poincare serileri kullanılarak oluşturulması

In this thesis, we construct holomorphic modular forms of integral weight greater than 2for the principle congruence subgroup ?(N ) by means of Poincare series. We startby providing the necessary background information on modular forms. Then, weshow that Poincare series are in fact holomorphic modular forms and we obtainexplicit formulas for their Fourier coefficients. For the special case when Poincareseries are Eisenstein series, their Fourier coefficients become relatively simple.We give Fourier coefficients of the Eisenstein series belonging to the principlecongruence subgroup. Finally, as an application of what has been studied, weconstruct Eisenstein series for the Hecke congruence supgroup.