= Prime Gamma 1 cusp counts and widths
{title2=$r_\infty=p-1,\quad d=(p^2-1)/2$}
For $p\ge5$, 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 $(p-5)(p-7)/24$.
Back to article page
