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Inspired by a paper of Tasaka, we study the relations between totally odd,motivic depth-graded multiple zeta values. Our main objective is to determinethe rank of the matrix $C_{N,r}$ defined by Brown. We will give new proofs for(conjecturally optimal) upper bounds on the rank of $C_{N,3}$ and $C_{N,4}$,which were first obtained by Tasaka. Finally, we present a recursive approachto the general problem, which reduces evaluating the rank of $C_{N,r}$ to anisomorphism conjecture.

Totally odd depth-graded multiple zeta values and period polynomials