So I have got a pretty complex equation (with different types of brackets) and it's too long, so I want to break the equation up to start a new line. The equation is:

```
\begin{document}
$$
Cl_f(\vec x):=\min\left\lbrace a\in\{1,\cdots,m\} : p_a Tr(F^{(n)}_a\rho^{(n)}_{\vec{x}})=\max_j\left\lbrace p_j Tr ( F^{(n)}_j\rho^{(n)}_{\vec{x}}), 1\le j\le m \right\rbrace\right\rbrace. \notag
$$
\end{document}

```

How do I start a new line in the equation when using `$$`? Say for eg., I want to break the equation up to start a new line after the colon sign (`:`), just before `p_a`. I would like the output to look something like:

```
Cl_f(\vec x):=\min\left\lbrace a\in\{1,\cdots,m\} :
              p_a Tr(F^{(n)}_a\rho^{(n)}_{\vec{x}})=\max_j\left\lbrace p_j Tr ( F^{(n)}_j\rho^{(n)}_{\vec{x}}), 1\le j\le m \right\rbrace\right\rbrace. \notag

```

I have tried using `\begin{align*}` but it's giving me funny error messages in the log (which I think it's to do with the bracket calls). I am good to use `$$`, `\begin{align*}` or any other method as long as I can get the output that I am after, with minimal packages that I need to load if possible.