Editing Modular form (section)

===Definition===
A modular form for {{mvar|G}} of weight ''k'' is a function on '''H''' satisfying the above functional equation for all matrices in {{mvar|G}}, that is holomorphic on '''H''' and at all cusps of {{mvar|G}}. Again, modular forms that vanish at all cusps are called cusp forms for {{mvar|G}}. The '''C'''-vector spaces of modular and cusp forms of weight ''k'' are denoted {{math|''M<sub>k</sub>''(''G'')}} and {{math|''S<sub>k</sub>''(''G'')}}, respectively. Similarly, a meromorphic function on ''G''\'''H'''<sup>∗</sup> is called a modular function for {{mvar|G}}. In case ''G'' = Γ<sub>0</sub>(''N''), they are also referred to as modular/cusp forms and functions of ''level'' ''N''. For {{math|''G'' {{=}} Γ(1) {{=}} SL(2, '''Z''')}}, this gives back the afore-mentioned definitions.