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The associative algebra of symplectic reflections $\mathcal H:= H_{1,\nu_1,\nu_2}(I_2(2m))$ based on the group generated by the root system $I_2(2m)$ hastwo parameters, $\nu_1$ and $\nu_2$. For every value of these parameters, thealgebra $\mathcal H$ has an $m$-dimensional space of traces. A given trace${\rm tr}$ is called degenerate if the associated bilinear form $B_{\rmtr}(x,y)={\rm tr}(xy)$ is degenerate. Previously, there were found all valuesof $\nu_1$ and $\nu_2$ for which there are degenerate traces in the space oftraces, and consequently the algebra $\mathcal H$ has a two-sided ideal. Weproved earlier that any linear combination of degenerate traces is a degeneratetrace. It turns out that for certain values of parameters $\nu_1$ and $\nu_2$,degenerate traces span a 2-dimensional space. We prove that non-zero traces inthis $2d$ space generate three proper ideals of $\mathcal H$.

Ideals generated by traces in the symplectic reflection algebra $H_{1,\nu_1, \nu_2}(I_2(2m))$. II