Prime Gamma 1 cusp counts and widths ($r_{\infty }=p-1,d=(p^2-1)/2$)

For $p\ge 5$, the Gamma 1 congruence subgroup has $(p-1)/2$ modular cusps of cusp width one and $(p-1)/2$ of cusp width $p$. Primitive columns modulo $p$, taken up to sign, are acted on by $(a,c)\mapsto (a+bc,c)$. The classes with $c=0$ have cusp width one, the others cusp width $p$. There are no effective elliptic stabilizers. The genus formula for a modular curve gives genus $(p-5)(p-7)/24$.