I'm self-studying representation theory for finite groups using "Group Theory and Quantum Mechanics" by Michael Tinkham. Most of it makes sense to me, but I'm having difficulty understanding what is meant by saying a function "belongs to a particular irreducible representation", or "has the symmetry of a particular irreducible representation". I assume this has something to do with a particular set of functions acting as a basis for an irreducible representation, but I still don't understand what is meant by "the symmetry of an irreducible representation". To make my question a bit more concrete, what do the last columns two columns in this character table (labeled "linear, rotations" and "quadratic") mean? I have a couple other questions, but they're more specific to this book. I understand it's a fairly popular text, so if someone has a copy of it handy and wouldn't mind entertaining another question or two, I'll post them in a follow up comment. Thanks!