, 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

H. Cohen and F. Strömberg, Modular Forms: A Classical Approach, Graduate Studies in Math, vol.179, 2017.

F. Diamond and J. Shurman, A first course in modular forms, Graduate Texts in Math, vol.228, 2005.

T. Miyake, Modular Forms, 1989.

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

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