  We show that there is a relationship between modular forms and totally odd
multiple zeta values, by relating the matrix $E_{N,r}$, whose entries are given
by the polynomial representations of the Ihara action, with even period
polynomials. We also consider the matrix $C_{N,r}$ defined by Brown and give a
new upper bound of the rank of $C_{N,4}$. This result gives support to the
uneven part of the motivic Broadhurst-Kreimer conjecture of depth 4.
