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?