  We show that if $G$ is a finite Abelian group and $f$ is an integer-valued
map on $G$ with algebra norm at most $M$ then there is some $L <
\exp(M^{4+o(1)})$, cosets of (possibly different) subgroups $W_1,...,W_L$, and
$s_1,...,s_L \in \{-1,1\}$ such that $f=\sum_i{s_i1_{W_i}}$.
