An Eisenstein series of rational weight

We study an Eisenstein series of weight $20\mathrm{/}9$, level $11$ whose multiplier system is the same as ${\eta }^{44\mathrm{/}9}(\tau ){\eta }^{-4\mathrm{/}9}(11\tau )$. We prove that it is a modular form and obtain its Fourier expansion.