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We describe images of the center of the dense globular cluster M15 (NGC~7078)
obtained with HST's WFPC2 instrument. Data taken in the F336W, F439W, and
F555W filters ($UBV$) yield a
color--magnitude diagram of $\sim3\times10^4$~stars in a 5~arcmin$^2$ region
within $r<2'$ (6.7$\,$pc) of the cluster center. Realistic simulated images
have been used to estimate photometric error and incompleteness in the star
counts.
The measurement error in color is $1\sigma\la0.05$~mag for stars with
$V<18$, increasing to $1\sigma\sim0.2$~mag at $V=20.5$, which is 1.5~mag
fainter than the main sequence turnoff.
The larger number of stars detected with WFPC2 (compared to WF/PC-1) result
in smaller Poisson errors in the determination of the star count profile.
The projected radial distribution of stars (after correction for
incompleteness and photometric bias/error)
is well represented by a power law: $N(r)\sim{r}^\alpha$, with
slope $\alpha=-0.7\pm0.15$, into radii less than 0\farcs3 (0.015$\,$pc).
Any flat core of radius larger than $1''$ (0.05$\,$pc) in the stellar
distribution is ruled out at the 99\% level.
Only 30 blue straggler candidates are identified from the $UBV$ data within
$r\la30''$, and we use the simulations to correct for contamination by
subgiant and turnoff stars. The specific frequency of blue straggler stars
(relative to red giant branch [RGB] and subgiant stars) in the central region
of M15 is $f_{\rm BSS}=0.05\pm0.02$ which is significantly lower than in other
dense clusters.
The incompleteness-corrected radial distribution of $19