On numerical characteristics of some bundles and their isomorphism classes on $\mathbb{P}^3$

We obtain formulas in the explicit form for the spectra of a family of stable rank $2$ vector bundles on $\mathbb{P}^3$ which isomorphism classes constitute the so-called Ein components in the Gieseker–Maruyama moduli scheme. We also obtain formulas in the explicit form for dimensions of the moduli space of the modified instanton bundles, and for their spectra. We show that Vedernikov and Hartshorne families in the Gieseker–Maruyama moduli scheme are particular cases of the Ein components.