References request: Ramanujan's tau function. Let $\Delta(z)=q\prod_{n=1}^{\infty} (1-q^n)^{24}=\sum_{n=1}^{\infty} \tau(n)q^n$, $q=e^{2\pi i z}$. How can one show the following using representation theory? $$ \tau(n)=\sum_S \frac{(a-b)(a-c)(a-d)(a-e)(b-c)(b-d)(b-e)(c-d)(c-e)(d-e)}{1!2!3!4!}, $$
where $S$ is the set of ordered tuples $(a,b,c,d,e)\in \mathbb{Z}^5 $ with
$$(a,b,c,d,e) \equiv (1,2,3,4,5) \pmod 5 $$ $$ a+b+c+d+e=0 $$ $$a^2+b^2+c^2+d^2+e^2=10n.$$ Thank you very much.