  In \cite{lafforgue2012chtoucas}, Vicent Lafforgue attaches a semisimple
Langlands parameter (or, what amounts to the same thing, a
$\hat{G}$-pseudocharacter) to every cuspidal automorphic representation of a
reductive group $G$ over the field of functions of a smooth projective
algebraic curve $X$ over a finite field. Hence, gets a decomposition of the
space of cusp forms. In this note, we show that in the case of $G = SL(n)$,
Lafforgue's decomposition coincides with the classical decomposition using
$L$-packets, and moreover, the number of ($G$-equivalence classes of)
extensions of an unramified Hecke character of $G$ to
$\hat{G}$-pseudocharacters serves as a natural upper bound on the multiplicity
of $SL(n)$.
