I'd like to ask the following MAGMA-question:
How to find the irreducible constituents of a Brauer character with MAGMA?
Let $G$ be a finite group. Moreover, let $k$ be a finite field of characteristic $p$, such that $p$ divides $|G|$. Furthermore suppose that $k$ is a splitting field for $G$.
Let $M$ be a $kG$-module with Brauer character $\phi$.
How can I find the multiplicities of the elements of IBr in $\phi$ with MAGMA?
Example ( This $k$ should be a splitting field for $G$ in char. 3.):
G:=Sym(6);
K:=GF(81);
PIMs:=ProjectiveIndecomposableModules(G,K);
sim:=IrreducibleModules(G,K);
IBr:=[BrauerCharacter(j) : j in sim];
proj3:=PIMs[3];
brchar:=BrauerCharacter(proj3);
Decomposition(IBr,brchar);
yielded
[
0,
0,
9/8,
0,
0,
0,
0
]
( 63/2, -15/4, 15/4, 0, 0, 0, 1/4, 0, 17/8, 0, 0 )
Unfortunately, I wasn't able to find my mistake. Any help is appreciated. Thank you very much.