On the vanishing of coefficients of $η^{26}

J.-P. Serre, in his paper [1], established a sufficient condition on $n$ for the $n$-th coefficient of the series ${\eta }^{26}$ to vanish. However, the question that whether this is a necessary condition remained unanswered. In this paper, using the theory of Hecke eigenforms explored by Serre, we prove some partial cases for the converse part.