In weights 2 and 3, the elliptic Kashiwara-Vergne Lie algebra has dimension 1 for even j and 0 for odd j in weight 2, and dimension floor((m-1)/2) - floor((m-1)/3) in weight 3 for odd m, confirming Enriquez' conjecture in these degrees.
Kontsevich, Formal (non)-commutative symplectic geometry , The Gelfand Mathematical Seminars, 1990-1992 (L
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The Elliptic Kashiwara-Vergne Lie algebra in low weights
In weights 2 and 3, the elliptic Kashiwara-Vergne Lie algebra has dimension 1 for even j and 0 for odd j in weight 2, and dimension floor((m-1)/2) - floor((m-1)/3) in weight 3 for odd m, confirming Enriquez' conjecture in these degrees.