We define traces associated to a weakly holomorphic modular form of arbitrary negative even integral weight and show that these traces appear as coefficients of certain weakly holomorphic forms of half-integral weight. If the coefficients of are integral, then these traces are integral as well. We obtain a negative weight analogue of the classical Shintani lift and give an application to a generalization of the Shimura lift.
"Integral traces of singular values of weak Maass forms." Algebra Number Theory 2 (5) 573 - 593, 2008. https://doi.org/10.2140/ant.2008.2.573