  In this article we show that the Euler equations, when linearized around a
low frequency perturbation to Couette flow, exhibit norm inflation in
Gevrey-type spaces as time tends to infinity. Thus, echo chains are shown to be
a (secondary) linear instability mechanism. Furthermore, we develop a more
precise analysis of cancellations in the resonance mechanism, which yields a
modified exponent in the high frequency regime. In addition it allows us to
remove a logarithmic constraint on the perturbations present in prior works by
Bedrossian, Deng and Masmoudi and to construct solutions which are initially in
a Gevrey class for which the velocity asymptotically converges in Sobolev
regularity but diverges in Gevrey regularity.
