Comparing Two Areas on a Parabola

The parabola $y=ax^2$ passes through the point $P(-1,1)$. Through the point $Q\left(-\dfrac 12,0\right)$, a line $l$ of positive slope meets the parabola at two points $M$ and $N$, with $M$ lying between $Q$ and $N$. The horizontal line through $M$ meets the line $OP$ at $A$ and the line $ON$ at $B$, where $O$ is the origin. Let $S_1$ and $S_2$ denote the areas of $\triangle PMA$ and $\triangle OAB$ respectively.

Compare $S_1$ with $3S_2$, and justify your answer.