What is a modular form (math)?

Question

What is a modular form, in simple terms?

What is a modular form, in simple terms? Is it some kind of function plotted on a graph?

Answer 1

Whee, uh, I doubt if this is something you heard about in high school, but here it goes: A modular form is a complex analytic function on the upper half-plane satisfying a number of conditions, and defined by two complex axes, so that they exist in hyperbolic space. They exhibit infinite symmetry under transformations of the type f(z) -> f[(az+b)/(cz+d)]. Related to elliptic functions, they appear in algebraic topology, string theory, and even in Mandelbrot sets. Here's the website about this last aspect, check out the color pictures:

Answer 2

I think it is the absolute form, where |-50| is the absolute form of (-50). |-50| = 50.

Answer 3

I don't think it can be made simple:
http://en.wikipedia.org/wiki/Modular_form