Beilinson–Bloch conjecture for modular-form motives

Let $E$ be a number field, let $f$ be the modular form under consideration, let $L(f\otimes E,s)$ be its complex $L$-function over $E$, and let $X_\mathfrak{p}(E)$ be the associated $F_\mathfrak{p}$-vector space defined in the paper. Beilinson–Bloch conjecture.

$$\dim_{F_\mathfrak{p}}\bigl(X_\mathfrak{p}(E)\bigr)=\operatorname{ord}_{s=\frac{k}{2}}L(f\otimes E,s).$$

This predicts that the dimension of the relevant motivic or Chow-theoretic realization equals the order of vanishing of the twisted $L$-function at the central point. The supplied context identifies the conjecture and its setting but does not state whether it has been resolved.