Highest-weight vectors of the moonshine module with non-zero graded trace

We study the space of graded traces (one-point correlation functions) of highest-weight vectors (primary fields) in the moonshine module. We define a family of highest-weight vectors with weight congruent to two modulo four and explicitly compute their graded traces. In particular, when their weight is at least 18, these highest-weight vectors have a non-zero graded trace.