  We give a coset realization of the vertex operator algebra $M(1)^+$ with
central charge $\ell$. We realize $M(1)^+$ as a commutant of certain affine
vertex algebras of level -1 in the vertex algebra $L_{C_{\ell}
^{(1)}}(-\tfrac{1}{2}\Lambda_0) \otimes L_{C_{\ell}
^{(1)}}(-\tfrac{1}{2}\Lambda_0)$. We show that the simple vertex algebra
$L_{C_{\ell} ^{(1)}}(-\Lambda_0)$ can be (conformally) embedded into $L_{A_{2
\ell -1} ^{(1)}} (-\Lambda_0)$ and find the corresponding decomposition. We
also study certain coset subalgebras inside $L_{C_{\ell} ^{(1)}}(-\Lambda_0)$.
