Let $S _ { n }$ be the sum of the first $n$ terms of an arithmetic sequence $\left\{ a _ { n } \right\}$. Given $a _ { 1 } = - 7 , S _ { 3 } = - 15$.\\
(1) Find the general term formula for $\left\{ a _ { n } \right\}$;\\
(2) Find $S _ { n }$ and the minimum value of $S _ { n }$.