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For each complex number $\nu$, an associative symplectic reflection algebra$\mathcal H:= H_{1,\nu}(I_2(2m+1))$, based on the group generated by rootsystem $I_2(2m+1)$, has an $m$-dimensional space of traces and an$(m+1)$-dimensional space of supertraces. A (super)trace $sp$ is said to bedegenerate if the corresponding bilinear (super)symmetric form$B_{sp}(x,y)=sp(xy)$ is degenerate. We find all values of the parameter $\nu$for which either the space of traces contains a degenerate nonzero trace or thespace of supertraces contains a degenerate nonzero supertrace and, as aconsequence, the algebra $\mathcal H$ has a two-sided ideal of null-vectors.The analogous results for the algebra $H_{1,\nu_1, \nu_2}(I_2(2m))$ are alsopresented.

Ideals generated by traces or by supertraces in the symplectic reflection algebra $H_{1,\nu}(I_2(2m+1))$