Sturm's Operator for Scalar Weight in Arbitrary Genus

In contrast to the well-known cases of large weights, Sturm’s operator does not realize the holomorphic projection operator for lower weights. We prove its failure for arbitrary Siegel modular forms of genus [Formula: see text] and scalar weight [Formula: see text]. This generalizes a result for genus two in [K. Maurischat and R. Weissauer, Phantom holomorphic projections arising from Sturm’s formula, preprint (2016)].