  The classical Dirichlet space is a complete Pick space, hence by a theorem of
Agler and McCarthy, there exists an embedding $b$ of the unit disc into a
$d$-dimensional ball such that composition with $b$ realizes the Dirichlet
space as a quotient of the Drury-Arveson space. We show that $d =\infty$ is
necessary, even if we only demand that composition with $b$ induces a
surjective map between the multiplier algebras.
