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 \(P^{*}(n), M(n), T^{*}(n), L(n), K(n), A(n)\) $P^{\ast }(n),M(n),T^{\ast }(n),L(n),K(n),A(n)$ , 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 \(2^a\cdot 5^\ell \) $2^a·5^{\ell }$ for \(P^{*}(n)\) $P^{\ast }(n)$ , modulo \(2^3\) $2^3$ for M(n) and \(T^*(n)\) $T^{\ast }(n)$ , where \(a=3, 4\) $a=3,4$ and \(\ell \ge 1\) $\ell \ge 1$ . For instance, we prove that for \(n\ge 0\) $n\ge 0$ , \(\begin{aligned} P^{*}(5^\ell (4n+3)+5^\ell -1)&\equiv 0\pmod {2^3\cdot 5^{\ell }}. \end{aligned}\) $$\begin{array}{cc}\hfill P^{\ast }(5^{\ell }(4n+3)+5^{\ell }-1)& \equiv 0(mod{2}^3·5^{\ell }).\hfill \end{array}$$ In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki: \(\begin{aligned} M(5n+4)\equiv 0\pmod {5},\quad T^{*}(5n+3)\equiv 0\pmod {5}. \end{aligned}\) $$\begin{array}{c}\hfill M(5n+4)\equiv 0(mod5),T^{\ast }(5n+3)\equiv 0(mod5).\end{array}$$