A Lower Bound for the Norm of the Theta Operator

L. Alayne Parson
1983 Mathematics of Computation  
The Poincaré theta operator maps the space of holomorphic functions with period one onto the space of cusp forms for a finitely generated Fuchsian group. It is easy to show that the norm of the operator does not exceed one. In the case of the classical modular group and weight six, it is now shown that the norm is bounded below by .927.
doi:10.2307/2007703 fatcat:6ubbl6lx3zedpdv6lhu55udwxm