I'd like to learn about modular forms. My background is mostly computational algebra and group theory, and I've had little-to-no training in complex analysis. I've briefly seen modular forms in a short literature review I did on Monstrous Moonshine. I've been scouting out various books, and most have a reasonably strong analytic focus.

While I'm happy to learn enough analysis to get into modular forms via the standard recommended textbooks, I was wondering:

Is there a good reference for learning modular forms that had a particularly algebraic or computational bent?

Modular Forms: A Computational Approach, by William A. Stein ? It is available on his home page at williamstein.org. – Chandan Singh Dalawat Jan 12 '12 at 11:59