A Modular Form Proof of the Irrationality of $\zeta \left(3\right)$

We present an expository proof of the irrationality of $\zeta \left(3\right)$ using modular forms of level 6. By constructing a suitable Eichler integral, we obtain a power series with controlled denominators and sufficiently large radius of convergence. Beukers’ irrationality criterion then implies that $\zeta \left(3\right)$ is irrational.