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For an affine Lie algebra $\hat{\mathfrak g}$ the coefficients of certainvertex operators which annihilate level $k$ standard $\hat{\mathfrakg}$-modules are the defining relations for level $k$ standard modules. In thispaper we study a combinatorial structure of the leading terms of theserelations for level $k=2$ standard $\hat{\mathfrak g}$-modules for affine Liealgebras of type $C_{n}\sp{(1)}$ and the main result is a construction ofcombinatorially parameterized relations among the coefficients of annihilatingfields. It is believed that the constructed relations among relations will playa key role in a construction of Groebner-like basis of the maximal ideal of theuniversal vertex operator algebra $V^ k_{\mathfrak g}$ for $k=2$.

Combinatorial relations among relations for level 2 standard $C_{n}\sp{(1)}$-modules