We develop Ladyzhenskaya-Prodi-Serrin type spectral regularity criteria for 3D incompressible Navier-Stokes equations in a torus. Concretely, for any $N > 0, let wN$ be the sum of all spectral components of the velocity fields whose wave numbers $|ki| > N for all i = 1, 2, 3$. Then, we show that for any $N > 0$, the finiteness of the Serrin type norm of $wN$ implies the regularity of the flow. It implies that if the flow breaks down in a finite time, the energy of the velocity fields cascades down to the arbitrarily large spectral components of $wN$ and corresponding energy spectrum, in some sense, roughly decays slower than $κ−2$