Let $\mathfrak{g}$ be a semisimple Lie algebra and $V_{\lambda}$ be the irreducible $\mathfrak{g}$module with highest weight $\lambda$. Are there some softwares which can compute the formal character $ch(V_{\lambda})=\sum_{\mu}dim(V_{\mu})e(\mu)$ explicitly? We can use Weyl formula. But it is difficult to compute the result in practice. Thank you very much.

The software package LiE is good for this. It is no longer maintained, but it has a lot of functionality, and the documentation is good. There is an online demonstration here. There is a bit of a learning curve, but it can do pretty much anything you want. Also you can write your own programs using the previously defined commands, so it is quite customizable. If you use Ubuntu or Debian, the software is already in the repositories and you just have to install it using the package manager. Otherwise you have to download the source files from the page I linked to and compile them yourself. 


You can use sage for this (and for many other things) See the following manual page: 

