Solution
= Solution
If $W\in SL(n,\mathbb Z)$, then both $W$ and
$$
W^{-1}=\operatorname{adj}(W)
$$
have integer entries. Thus $q'=Wq$ maps $\mathbb Z^n$ into itself, and the inverse map shows that it maps onto all of $\mathbb Z^n$.
Writing the source contraction as $j^Ta$, with $j'=Wj$, invariance requires
$$
j'^Ta'=j^Ta.
$$
Hence
$$
j^TW^Ta'=j^Ta
$$
for every current, so
$$
\boxed{a'=W^{-T}a},
\qquad
\boxed{a=W^Ta'}.
$$