Let $\Gamma$ be a cofinite lattice in $PSL(2,\mathbb{R})$ with torsion subgroup $H$.
Is the a uniform bound on the cardinality of $H$?
Let $\Gamma$ be a cofinite lattice in $PSL(2,\mathbb{R})$ with torsion subgroup $H$. Is the a uniform bound on the cardinality of $H$? 


There are triangle groups $(2, 3, n)$ for any $n>6,$ so I would say the answer is NO 

