  For a subspace $W$ of a vector space $V$ of dimension $n$, the Schur-product
space $W^{\langle k\rangle}$ for $k \in \mathbb{N}$ is defined to be the span
of all vectors formed by the component-wise multiplication of $k$ vectors in
$W$. It is well known that repeated applications of the Schur product to the
subspace $W$ creates subspaces $W, W^{\langle 2 \rangle}, W^{\langle 3
\rangle}, \ldots$ whose dimensions are monotonically non-decreasing. However,
quantifying the structure and growth of such spaces remains an important open
problem with applications to cryptography and coding theory. This paper
characterizes how increasing powers of constacyclic codes grow under the Schur
product and gives necessary and sufficient criteria for when powers of the code
and or dimension of the code are invariant under the Schur product.
