  This paper provides yet another look at the mixed fractional Brownian motion
(fBm), this time, from the spectral perspective. We derive an approximation for
the eigenvalues of its covariance operator, asymptotically accurate up to the
second order. This in turn allows to compute the exact $L_2$-small ball
probabilities, previously known only at logarithmic precision. The obtained
expressions show an interesting stratification of scales, which occurs at
certain values of the Hurst parameter of the fractional component. Some of them
have been previously encountered in other problems involving such mixtures.
