  We present a power spectrum analysis of the ALMA Spectroscopic Survey Large
Program (ASPECS LP) data from 84 to 115 GHz. These data predominantly probe
small-scale fluctuations ($k=10$-$100$ h Mpc$^{-1}$) in the aggregate CO
emission in galaxies at $1 \lesssim z \lesssim 4$. We place an integral
constraint on CO luminosity functions (LFs) in this redshift range via a direct
measurement of their second moments in the three-dimensional (3D) auto-power
spectrum, finding a total CO shot noise power
$P_{\textrm{CO,CO}}(k_{\textrm{CO(2-1)}}) \leq 1.9\times10^2$ $\mu$K$^2$ (Mpc
h$^{-1}$)$^3$. This upper limit ($3\sigma$) is consistent with the observed
ASPECS CO LFs in Decarli et al. 2019, but rules out a large space in the range
of $P_{\textrm{CO,CO}}(k_{\textrm{CO(2-1)}})$ inferred from these LFs, which we
attribute primarily to large uncertainties in the normalization $\Phi_*$ and
knee $L_*$ of the Schechter-form CO LFs at $z > 2$. Also, through power
spectrum analyses of ASPECS LP data with 415 positions from galaxies with
available optical spectroscopic redshifts, we find that contributions to the
observed mean CO intensity and shot noise power of MUSE galaxies are largely
accounted for by ASPECS blind detections, though there are $\sim20$%
contributions to the CO(2-1) mean intensity due to sources previously
undetected in the blind line search. Finally, we sum the fluxes from individual
blind CO detections to yield a lower limit on the mean CO surface brightness at
99 GHz of $\langle T_{\textrm{CO}} \rangle = 0.55\pm0.02$ $\mu$K, which we
estimate represents $68$-$80$% of the total CO surface brightness at this
frequency.
