Class number formula conjecture for split primes 7 and 11

Let $K_d = \mathbb{Q}(\sqrt{-d})$ be an imaginary quadratic field in which $(p)=\mathfrak{p}\mathfrak{p}'$ splits, where $p=7$ or $11$. Let $\mathfrak{f}=\mathfrak{p}'$ be a first-degree prime ideal, write $-d=d_Kf^2$, and assume $N\mathfrak{p}=p$. Put $\mathcal{O}=\textsf{R}_{-d}$ and define

$$\tau_{\mathfrak{p}}=\left(\frac{F_d/K_d}{\mathfrak{p}}\right),$$

where $F_d$ is the inertia field for $\mathfrak{p}$ in the extended ring class field $L_{\mathcal{O},p}=\Sigma_p\Omega_{pf}$. Define

$$\mathfrak{D}_{n,p}=\Big\{-d\ \bigg|\left(\frac{-d}{p}\right)=+1\ \wedge \operatorname{ord}(\tau_{\mathfrak{p}})=n\Big\}.$$

Class number formula conjecture. For $n>1$,

$$\sum_{-d\in\mathfrak{D}_{n,p}}h(-d)=\frac{2}{\varphi(\mathfrak{f})}\sum_{k\mid n}\mu(n/k)p^k.$$

This conjecture extends the class-number formulas obtained by the same method for $p=2,3,5$ to the cases $p=7$ and $p=11$. Its status is not resolved in the supplied source context.