  Let $f$ be a holomorphic cusp form of integral weight $k \geq 3$ for
$\Gamma_{0}(N)$ with nebentypus character $\psi$. Generalising work of Kohnen
and Raghuram we construct a kernel function for the $L$-function $L(f,\chi,s)$
of $f$ twisted by a primitive Dirichlet character $\chi$ and use it to show
that the average $\sum_{f \in
S_{k}(N,\psi)}\frac{L(f,\chi,s)}{<f,f>}\bar{a_{f}(1)}$ over an orthogonal basis
of $S_{k}(N,\psi)$ does not vanish on certain line segments inside the critical
strip if the weight $k$ or the level $N$ is big enough. As another application
of the kernel function we prove an averaged version of Waldspurger's theorem
relating the central critical value of the $D$-th twist ($D < 0$ a fundamental
discriminant) of the $L$-function of a cusp form $f$ of even weight $2k$ to the
square of the $|D|$-th Fourier coefficient of a form of half-integral weight
$k+1/2$ associated to $f$ under the Shimura correspondence.
