The $p=2$ ghost conjecture for modular-form slopes

Let $N$ be a positive integer and let $\kappa\in\mathcal{W}$. Let $G_\kappa^{\circ}$ be the specialization of the modified ghost series for $p=2$, let $P_\kappa$ be the characteristic power series of the $U_2$-operator, and write $\operatorname{NP}$ for the Newton polygon. The prime $2$ is $\Gamma_0(N)$-regular when the corresponding regularity condition holds.

The $p=2$ ghost conjecture. If $2$ is $\Gamma_0(N)$-regular, then

$$\operatorname{NP}(G_\kappa^{\circ})=\operatorname{NP}(P_\kappa)$$

for every $\kappa\in\mathcal{W}$.

The modified series incorporates extra multiplicities at the relevant weight-space points and is designed to match the observed boundary slopes for level $\Gamma_1(8N)$. The assertion extends the ghost-series prediction to the $p=2$ setting.