Computing aspects of modular forms

This thesis gives an expanded description of modular forms. Starting from modular group and congruence subgroup the theory of modular forms is constructed and the origins of modular forms are given. Classification of modular form spaces are done. Using the classifications, the discussion about computing aspects are given. For computing purposes the theory of modular and Manin symbols are built and the relations between symbols and forms are given. The problem of explicit computing and creating a basis for a modular forms space are done in this thesis. SAGE, the open source algebra program, is used throughout the chapters to exemplify the given theories.