What's so special about the number 24 in the definition of the Ramanujan tau function?

Question

I'm learning about the Ramanujan tau function $\tau \colon \mathbb{N} \to \mathbb{Z}$ defined by $$\tau(1)q + \tau(2)q^2 + \tau(3)q^3 + \ldots = q \prod_{n = 1}^{\infty} \left(1 - q^n\right)^{24}.$$ However, I'm confused why the number $24$ is so special here. What if we used a different number instead of $24?$ All of the properties of the Ramanujan tau function I could find either had nothing to do with $24$ (such as the property that $\tau$ is multiplicative) or had some specific numbers in them.

Answer 1

$24$ is the value such that $\Delta$ is a weight $k$ modular form with only one simple zero on the modular curve (at $\infty$).

Then, let $f$ be another weight $k$ cusp form. So $\frac{f}{\Delta}$ is a weight $0$ modular form, by the maximum modulus principle it has to be constant.

For each Hecke operator $T_n \Delta$ is a weight $k$ cusp form, thus equal to $a_n \Delta$ for some $a_n$, which has to be the $n$-th coefficient of $\Delta$.

Whence the coefficients of $\Delta$ are multiplicative.