  Let $\phi_{\sqrt{2m}}(z)=\sum_{n\in\Z} a_n z^{-n-m}, m\in\N$ be bosonic
vertex operator, $L$ some irreducible representation of the vertex algebra
$\A_{(m)}$, associated with one-dimensional lattice $\Zl$, generated by vector
$l$, $\bra l,l \ket=2m$. Fix some extremal vector $v\in L$. We study the
principle subspace $\C[a_i]_{i\in\Z}\cdot v$ and its finitization
$\C[a_i]_{i>N}\cdot v$. We construct their bases and find characters. In the
case of finitization basis is given in terms of Jack polynomials.
