  We set up a simple trace formula giving the number of holomorphic newforms of
weight $k$ and level $N$ whose local representation type at each $p|N$ is a
fixed supercuspidal representation $\sigma_p$ of
$\operatorname{GL}_2(\mathbf{Q}_p)$. We evaluate the formula in detail in the
case where each $\sigma_p$ has conductor $\le p^3$. We also compute the traces
of Hecke operators on the span of these newforms. The technical heart of the
paper is the calculation of elliptic orbital integrals attached to certain
supercuspidal matrix coefficients. Some applications are given to biases among
root numbers of newforms.
