Bloch–Kato Tamagawa number conjecture for modular forms

Let $f$ be a newform of even weight $k$, let $0\leq j\leq k-2$, and assume $L(f,j+1)\neq0$. Let $\Omega^{(-1)^{j+1}}$ denote the relevant period, $u_{j+1}$ the associated unit factor, $\operatorname{Tam}(j+1)$ the Tamagawa factor, $\Sha(j+1)$ the relevant Shafarevich–Tate group, and $H^0_{\mathbb Q}(\cdot)$ the indicated degree-zero Galois cohomology groups. Bloch–Kato Tamagawa number conjecture. One has

$$\frac{L(f,j+1)}{(2\pi i)^{j+1} \Omega^{(-1)^{j+1}}}=u_{j+1}\times\frac{\operatorname{Tam}(j+1)\,\#\Sha(j+1)}{\#H^0_{\mathbb Q}(j+1)\,\#H^0_{\mathbb Q}(k-1-j)}=:C(j+1).$$

This is a special case of the Bloch–Kato conjectural interpretation of critical motivic $L$-values through Galois cohomology and Selmer groups. The source presents it as a conjecture for the modular-form setting; the supplied text gives no resolution status.