Pseudo-nullity conjecture for fine Selmer groups of elliptic modular forms

Let $L_\infty$ be a $\mathbb{Z}_{p}^{2}$-extension of a number field $F$ containing the cyclotomic $\mathbb{Z}_{p}$-extension $F^{\mathrm{cyc}}$. Let $G=\operatorname{Gal}(L_\infty/F)$, and let $Y(A_f/L_\infty)$ be the Pontryagin dual of the fine Selmer group attached to the modular form representation $A_f$. Modular-form pseudo-nullity conjecture. The module $Y(A_f/L_\infty)$ is pseudo-null over

$$\mathbb{Z}_{p}[[G]].$$

This is the analogue for modular forms of the Coates–Sujatha pseudo-nullity conjecture for abelian varieties. It is stated as a conjecture and remains open in the generality given.