  The study of this paper is inspired by the conjecture of Zagier on the
explicit dimension formula for the space of the same weight double zeta values
in terms of the dimension of cusp forms for SL_{2}(Z). Our main result is to
devise an effective criterion for computing the dimension of the same weight
double zeta values over a rational function field F_{q}(theta) in positive
characteristic. Contrary to the Zagier's conjecture, the analogue of Zagier's
conjectural dimension provides a lower bound for the dimension of the double
zeta values when the weight is $A$-even.
