We present the deepest optical color-magnitude diagram ( CMD ) to date of the local elliptical galaxy M32 .
We have obtained F 435 W and F 555 W photometry based on Hubble Space Telescope ACS/HRC images for a region 110 \arcsec from the center of M32 ( F1 ) and a background field ( F2 ) about 320 \arcsec away from M32 center .
Due to the high resolution of our Nyquist-sampled images , the small photometric errors , and the depth of our data ( the color-magnitude diagram of M32 goes as deep as F 435 W \sim 28.5 at 50 % completeness level ) we obtain the most detailed resolved photometric study of M32 yet .
Deconvolution of HST images proves to be superior than other standard methods to derive stellar photometry on extremely crowded HST images , as its photometric errors are \sim 2 \times smaller than other methods tried .

The location of the strong red clump in the CMD suggests a mean age between 8 and 10 Gyr for [ \mathrm { Fe / H } ] = -0.2 dex in M32 .
We detect for the first time a red giant branch bump and an asymptotic giant branch bump in M32 which , together with the red clump , allow us to constrain the age and metallicity of the dominant population in this region of M32 .
These features indicate that the mean age of M32 ’ s population at \sim 2 \arcmin from its center is between 5 and 10 Gyr .
We see evidence of an intermediate-age population in M32 mainly due to the presence of asymptotic giant branch stars rising to \mathrm { M } _ { F 555 W } \sim - 2.0 .
Our detection of a blue component of stars ( blue plume ) may indicate for the first time the presence of a young stellar population , with ages of the order of 0.5 Gyr , in our M32 field .
However , it is likely that the brighter stars of this blue plume belong to the disk of M31 rather than to M32 .
The fainter stars populating the blue plume indicate the presence of stars not younger than 1 Gyr and/or blue straggler stars in M32 .
The CMD of M32 displays a wide color distribution of red giant branch stars indicating an intrinsic spread in metallicity with a peak at [ \mathrm { Fe / H } ] \sim - 0.2 .
There is not a noticeable presence of blue horizontal branch stars , suggesting that an ancient population with [ \mathrm { Fe / H } ] < -1.3 does not significantly contribute to the light or mass of M32 in our observed fields .
M32 ’ s dominant population of 8–10 Gyr implies a formation redshift of 1 \lesssim z _ { f } \lesssim 2 , precisely when observations of the specific star formation rates and models of ‘ ‘ downsizing ’ ’ imply galaxies of M32 ’ s mass ought to be forming their stars .
Our CMD therefore provides a ‘ ‘ ground-truth ’ ’ of downsizing scenarios at z = 0 .

Our background field data represent the deepest optical observations yet of the inner disk and bulge of M31 .
Its CMD exhibits a broad color spread of red giant stars indicative of its metallicity range with a peak at [ \mathrm { Fe / H } ] \sim - 0.4 dex , slightly more metal-poor than M32 in our fields .
The observed blue plume consists of stars as young as 0.3 Gyr , in agreement with previous works on the disk of M31 .
The detection of bright AGB stars reveals the presence of intermediate-age population in M31 , which is however less significant than that in M32 at our field ’ s location .