CUBIC LEVEL ANALOGUE OF RAMANUJAN'S EISENSTEIN SERIES IDENTITIES

Let $Q_n=1+240\sum_{k=1}^{\infty} \frac{k^3q^{nk}}{1-q^{nk}}$. On page 51-53 of his lost notebook, Ramanujan recorded very interesting identities which relates $Q_1$, $Q_5$, $Q_7$ with his theta functions. In this article, we establish analogous identities with respect to $Q_1$ and $Q_3$.