, and in particular it proves that these values are rational numbers, a theorem due to C.-L. Siegel as an immediate consequence of Theorem 3.41. An example is as follows: There exist three software packages which are able to compute with modular forms: magma, Sage, and Pari/GP since the spring of, 2018.

, Creation of modular form spaces: mfinit, mfdim (dimension of the space), mfbasis (random basis of the space), mftobasis (decomposition of a form on the mfbasis), mfeigenbasis (basis of normalized eigenforms). Searching for modular forms with given Fourier coefficients: mfeigensearch, mfsearch. Expansion of F| k ?: mfslashexpansion. Numerical functions: mfeval (evaluation at a point in H or at a cusp), mfcuspval (valuation at a cusp), Pari/GP commands with little or no explanation (which is available by typing ? or ??): we encourage the reader to read the tutorial tutorial-mf available with the distribution and to practice with the package

, Note that for now Pari/GP is the only package for which these last functions

Modular Forms: A Classical Approach, Graduate Studies in Math, vol.179, 2017. ,

A first course in modular forms, Graduate Texts in Math, vol.228, 2005. ,

, Modular Forms, 1989.

Introduction to the arithmetic theory of automorphic functions, Publ. Math. Soc. Japan, vol.11, 1994. ,

Elliptic modular forms and their applications, in "The 1-2-3 of modular forms, pp.1-103, 2008. ,