Selberg's eigenvalue conjecture for principal congruence surfaces

For the principal congruence surface $X_N=\Gamma(N)\backslash\mathbb{H}^2$, let $\mathcal{C}(X_N)$ denote the space of cusp forms, and let $\lambda_1^{\mathrm{cusp}}(X_N)$ be the minimal eigenvalue of the Laplacian $\Delta_{X_N}$ on this space.

Selberg's eigenvalue conjecture. For every $N$,

$$\lambda_1^{\mathrm{cusp}}\Big(\Gamma(N) \backslash \mathbb{H}^2\Big) \geq \frac{1}{4}.$$

Selberg's conjecture concerns the optimal uniform spectral gap for cusp-form eigenvalues on these congruence surfaces. The source does not state a resolution, so its status is left open.