On \(4^\alpha \)-regular overpartitions modulo powers of 2

In this study, we explore novel arithmetic properties of the number of overpartitions of n whose parts are not divisible by \(\ell \) $\ell$ , denoted by \(\overline{A}_\ell (n)\) ${\overline{A}}_{\ell }(n)$ . Notably, we present a series of Ramanujan-type congruences modulo powers of 2 for \(\overline{A}_{4^\alpha } (n)\) ${\overline{A}}_{4^{\alpha }}(n)$ within specific arithmetic progressions.