This is a problem book on modular forms, aimed at graduate students and researchers with an interest in computational aspects of the subject. It assumes some familiarity with classical modular forms, with a brief review provided in the opening chapter. The text is organized into largely independent chapters, each devoted to a specific topic. The first part presents the necessary background and a collection of problems, many involving implementations in Pari/GP; the second part provides solutions and additional material. Full implementations in Pari/GP are available on GitHub.

Topics include differential operators, Eisenstein series, eta quotients, exact computation of L-values at negative integers (notably via half-integral weight methods), orthogonal polynomials and their applications, Fourier expansions at general cusps, nonholomorphic Eisenstein series and related identities, and aspects of complex multiplication, Hauptmoduln, and special values. All implementations are provided as Pari/GP scripts, and the exercise–solution format drives computational engagement.

Henri Cohen is an emeritus professor at the University of Bordeaux. He is best known for leading the team that created the award-winning PARI/GP computer algebra system and for writing a number of bestselling graduate texts on computational and general number theory as well as for important theoretical contributions to number theory.

Wissam Ghantous is an assistant professor at the University of Central Florida. His current work mainly deals with computational aspects of elliptic curves and modular forms as well as the application of number theory to cryptography.