The computer algebra packages I know most about are pari and magma. These packages are as different as chalk and cheese, but both are excellent for doing computational number theory. Pari is free and open source, magma is not free and not open source. This has all the obvious consequences. I love them both.

I make some very unwieldy conjectures about slopes of modular forms, in my paper "Questions about slopes of modular forms". I also wrote some similarly unwieldy programs to compute specific instances of these conjectures.

Here is a magma script, Tpprog.m that computes these conjectural slopes.

Here is a pari script, Tpprog.g that also computes these conjectural slopes. But here the situation is a little more complicated. The conjectures involve dimensions of spaces of certain modular forms, and these functions are inbuilt into magma but not into pari. So to get the pari scripts to work, one needs to load Bruce Kaskel's script genusn.g for computing dimensions of various spaces of forms for Gamma_0(N) and Gamma_1(N), and also my script DimensionSk.g (*** new version 14 Feb 2002 with a bug fix ***) for computing dimensions of various spaces of forms with non-trivial character. Thanks to Fernando Gouvea for spotting the bug in a previous version of DimensionSk.g .