Conjecture on the orientability order of the universal complex line bundle for EO-theory

Let $\Gamma$ be a formal group of height $n=(p-1)k$, and let $\mathbb{C}$ denote the complex line bundle appearing in the definition of the orientability order $\Theta$. Orientability-order conjecture.

$$\Theta(\mathrm{EO}_{\Gamma},\mathbb{C})=p^k.$$

This conjectures the exact value of the $\mathrm{EO}_{\Gamma}$-orientability order in the case that the height is divisible by $p-1$. Previously known results give non-sharp bounds in some cases, including height $p-1$ and at the prime $2$, so the asserted equality remains open here.