Helton-Howe trace formula gives an explicit description of the traces of antisymmetric sums of Toeplitz operators on the Bergman space. On a submodule of the Bergman module with relatively nice zero locus, previous results show that the cross commutators between the generalized Toeplitz operators with coordinate symbols belong to some Schatten class. A natural question is whether the same Helton-Howe trace formula remain true for such submodules. We answer this question in affirmative, using finite rank approximation and dilation techniques

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