Modular Forms And Constructions

In this paper we first study the properties of modular forms and cusp forms for the full modular group, then consider the constructions of the modular or cusp forms for its congruence subgroups. We make use of Eisenstein series and Poincare series to give some basic modular forms. Combining with the dimensional formulas of modular forms and the constructions of the cusp forms, we get some identities.