In general Sato-Tate group labels have the form $w.d.r.c.ns$, where
- $w$ is the weight (nonnegative integer);
- $d$ is the degree (positive integer, even if $w$ is odd);
- $r$ is the real dimension (nonnegative integer);
- $c$ is the number of components (positive integer);
- $n$ is the second digit of the GAP id $[c,n]$ of the component group (positive integer);
- $s$ is a lowercase letter (or string of lowercase letters) used to break ties; it has no intrinsic meaning.
When $w=0$ we necessarily have $r=0$ and may omit $r$. When $w=0$ and $d=1$ there is exactly one Sato-Tate group for each value of $c$ and we may omit $n$ and $s$.