Stronger convolution q-congruences extending Theorems 7 and 8

Let $n$ be a positive odd integer, and let $c_q(k)$ be the sequence defined in Theorem 7. Let $[n]$ denote the $q$-integer and let $\Phi_n(q)$ denote the $n$th cyclotomic polynomial. The strengthened convolution q-congruence.

$$\sum_{k=0}^{n-1}\sum_{j=0}^{k}c_q(j)c_q(k-j) \equiv \begin{cases} [n]^2\dfrac{(q^2;q^4)_{(n-1)/4}^4}{(q^4;q^4)_{(n-1)/4}^4}\pmod{[n]^2\Phi_n(q)^2},&n\equiv1\pmod4,\\ 0\pmod{[n]^2\Phi_n(q)^4},&n\equiv3\pmod4. \end{cases}$$

This is presented as a stronger version of Theorem 7, while the surrounding text also mentions Theorem 8; the supplied statement itself defines $c_q(k)$ only by reference to Theorem 7.