Three-dimensional lens space as a circle bundle ($S^1\to L(p)\to S^2$)

The diagonal quotient $L(p)=S^3/(\mathbb{Z}/p)$ is the unit circle bundle of a complex line bundle over $S^2$ whose Euler class is $p$ times a generator. Its Gysin sequence giveswhile $H^j(L(p);{\mathbb{F}}_p)\cong {\mathbb{F}}_p$ for $0\le j\le 3$.