Let V be the vector space of all polynomials with a real coefficient of degree at most 10. Considering elements of V as functions from R to R, define \(W = \left\{ {P \in V{\rm{|}}\mathop \smallint \nolimits_0^1 P\left( x \right)dx = 0} \right\}\) be a subspace of V, then dim W is ________.