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If $G$ is a finite Coxeter group, then symplectic reflection algebra$H:=H_{1,\eta}(G)$ has Lie algebra $\mathfrak {sl}_2$ of inner derivations andcan be decomposed under spin: $H=H_0 \oplus H_{1/2} \oplus H_{1} \oplus H_{3/2}\oplus ...$. We show that if the ideals $\mathcal I_i$ ($i=1,2$) of all thevectors from the kernel of degenerate bilinear forms $B_i(x,y):=sp_i(x\cdoty)$, where $sp_i$ are (super)traces on $H$, do exist, then $\mathcalI_1=\mathcal I_2$ if and only if $\mathcal I_1 \bigcap H_0=\mathcal I_2 \bigcapH_0$.

Connection between the ideals generated by traces and by supertraces in the superalgebras of observables of Calogero models