= Solution
The integrated spectrum combines <stars> moving toward and away from us within the <galaxy>, broadening their absorption by <Doppler shifts>. Assuming instrumental and individual-stellar widths have been removed or are negligible, the line-of-sight <velocity dispersion> is
$$
\boxed{\sigma_v\simeq c\frac{0.4}{874.0}\simeq137\,\mathrm{km\,s^{-1}}.}
$$
The angular <half-light radius> at the low-redshift distance is $R_e\simeq2.35$ kpc. For a pressure-supported, approximately isotropic equilibrium spheroid with a standard structural virial coefficient of order five, use
$$
\boxed{M_{\rm dyn}\sim\frac{5R_e\sigma_v^2}G\simeq5.1\times10^{10}M_\odot.}
$$
The coefficient represents assumed <density> profile, aperture and orbital structure; a different reasonable <mass> estimator changes the result by an order-unity factor. Treating $D$ as a <luminosity> distance and using $D_A=D_L/(1+z)^2$ would reduce the <radius> and <mass> by about four percent here.
The <distance modulus> is about $34.93$. The magnitude \b[within] $R_e$ therefore corresponds to $M_{V,\rm half}\simeq-19.23$ and
$$
L_{\rm half}/L_\odot=10^{0.4(4.7-M_{V,\rm half})}\simeq3.74\times10^9.
$$
Doubling the half-light <luminosity> gives
$$
\boxed{L_{V,\rm total}\simeq7.5\times10^9L_{V,\odot},\qquad
\frac{M_{\rm dyn}}{L_{V,\rm total}}\simeq6.9\,\frac{M_\odot}{L_{V,\odot}}.}
$$
This ratio is compatible with an old stellar population plus possible <dark matter>. It is larger than a solar-like <mass-to-light ratio>, but does not by itself isolate a unique dark-matter fraction: stellar age, initial <mass> function, anisotropy and the virial coefficient are not specified. Counting the quoted half-light magnitude as the total would incorrectly double the inferred ratio.
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