  We compute the central critical value of the triple product $L$-function
associated to three cusp forms $f_1,f_2,f_3$ with trivial character for groups
$\Gamma_0(N_i)$ with square free levels $N_i$ not all of which are $1$ and
weights $k_i$ satisfying $k_1\ge k_2\ge k_3$ and $k_1<k_2+k_3$. This
generalizes work of Gross and Kudla and gives an alternative classical proof of
their results in the case $N_1=N_2=N_3$ with $k_1=k_2=k_3=2$.
