The term modular form is used to describe several types of functions which have a certain type of transformation property and growth condition. The theory of modular forms, although in complex analysis, is intricately connected to areas of number theory, algebraic geometry, combinatorics, algebraic topology, and mathematical physics.
Below you can browse classes of modular forms currently in the LMFDB.
Holomorphic Cusp Forms (on \(\GL(2)\) over \(\Q\))
Hilbert Modular Forms (on \(\GL(2)\) over totally real fields)