Güneş, Çisem2016-01-082016-01-082010http://hdl.handle.net/11693/15070Ankara : The Department of Mathematics and the Institute of Engineering and Science of Bilkent University, 2010.Thesis (Master's) -- Bilkent University, 2010.Includes bibliographical references leaves 63-65.In this thesis, we construct holomorphic modular forms of integral weight k > 2 for the principle congruence subgroup Γ( ¯ N) by means of Poincar´e series. We start by providing the necessary background information on modular forms. Then, we show that Poincar´e series are in fact holomorphic modular forms and we obtain explicit formulas for their Fourier coefficients. For the special case when Poincar´e series are Eisenstein series, their Fourier coefficients become relatively simple. We give Fourier coefficients of the Eisenstein series belonging to the principle congruence subgroup. Finally, as an application of what has been studied, we construct Eisenstein series for the Hecke congruence supgroup.vii, 65 leavesEnglishinfo:eu-repo/semantics/openAccessPoincar´e seriesCongruence subgroupsModular groupCusp formsModular formsEisenstein seriesQA243 .G85 2010Forms, Modular.Poincaré series.ThesisB122453