Buzzard's classical 2-adic Newton polygon conjecture for level-1 cusp forms

Let $k\geq12$ be even, let $S_k=S_k(\Gamma_0(1),\mathbf{Q})$ be the space of level-$1$ cusp forms of weight $k$, and let $m=\dim S_k$. For a polynomial with rational coefficients, its 2-adic Newton polygon means its Newton polygon over the 2-adic numbers. Buzzard's classical slope conjecture. The 2-adic Newton polygon of

$$\operatorname{det}(1-XT_2)$$

on $S_k$ equals the 2-adic Newton polygon of

$$1+\sum_{n=1}^{m}X^n\prod_{j=1}^{n}\frac{2^{2j}(k-8j)!(k-8j-3)!(k-12j-2)}{(k-12j)!(k-6j-1)!}.$$

The conjecture was verified numerically for all $k\leq2048$ in the source. Via Coleman's control theorems, it is related to the slopes of finite-slope overconvergent cusp forms at tame level $1$; its general validity remains open.