On some new arithmetic properties of certain restricted color partition functions

Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely \(P^{*}(n), M(n), T^{*}(n), L(n), K(n), A(n)\), and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo \(2^a\cdot 5^\ell \) for \(P^{*}(n)\), modulo \(2^3\) for M(n) and \(T^*(n)\), where \(a=3, 4\) and \(\ell \ge 1\). For instance, we prove that for \(n\ge 0\),

$$\begin{aligned} P^{*}(5^\ell (4n+3)+5^\ell -1)&\equiv 0\pmod {2^3\cdot 5^{\ell }}. \end{aligned}$$

In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki:

$$\begin{aligned} M(5n+4)\equiv 0\pmod {5},\quad T^{*}(5n+3)\equiv 0\pmod {5}. \end{aligned}$$