4. Given the ellipse $C: \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1(a>b>0)$ with left and right foci $F_{1}$ and $F_{2}$, upper and lower vertices $B_{1}$ and $B_{2}$, and right vertex $A$, the line $A B_{1}$ intersects $B_{2} F_{1}$ at point D. If $2\left|A B_{1}\right|=3\left|B_{1} D\right|$, then the eccentricity of the ellipse $C$ is $\qquad$
4. $\frac{1}{4}$.

Connect $B_{1} F_{2}$. Then $B_{1} F_{2} / / B_{2} D$.
$$
\begin{array}{l}
\text { Hence } \frac{\left|A B_{1}\right|}{\left|B_{1} D\right|}=\frac{\left|A F_{2}\right|}{\left|F_{1} F_{2}\right|} \\
\Rightarrow \frac{3}{2}=\frac{a-c}{2 c} \\
\Rightarrow e=\frac{c}{a}=\frac{1}{4} .
\end{array}
$$