  Variations at the event horizon structure of a black hole will emit the
signals of the gravitational wave echoes associated with the ringdown phase of
the binary black hole merger. In this work, combining the mass model of M87 and
the Einasto profile for a dark matter halo, we construct one solution of the
black holes in a dark matter halo through the relativistic analysis, which
includes black hole for the case $a \leq 2M$ and the travesable wormhole for
the case $a>2M$. Then, we test this solution in the axial gravitational
perturbation and calculated their gravitational ringings of this black hole,
that is the quasinormal mode (QNM). Where, when the geometric parameter $a>2M$,
a series of gravitational wave echoes appear after the QNM, and the distinctive
feature of the gravitational wave echoes is the double barrier feature.
Besides, we also study the impacts of the shape parameters of the Einasto
profile both on the QNM and gravitational wave echoes of this black hole, and
extract their frequencies using the WKB method and Prony method. In particular,
from the perspective that the QNM frequencies between different black hole
parameters are distinguishable, we give an upper limit for the shape parameters
of the Einasto profile, which is approximately $\alpha<0.20$. These signals of
the gravitational wave echoes based on this black hole in a dark matter halo
may be detected in the near future, and these characteristics in the time
evolution of the gravitational wave echoes can serve as local measurements of
dark matter.
