  In this paper, we consider $L$-functions of modular forms of weight 3, which
are products of the Jacobi theta series, and express their special values at
$s=3$, $4$ in terms of special values of Kamp\'e de F\'eriet hypergeometric
functions. Moreover, via $L$-values, we give some relations between special
values of Kamp\'e de F\'eriet hypergeometric functions and generalized
hypergeometric functions.
