, 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
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