Given an integral lattice $\Lambda$ of rank $n$ and a finite sequence $m_1
\leq m_2 \leq ... \leq m_k$ of natural numbers we construct a modular form
$\Theta_{m_1,m_2,...,m_k,\Lambda}$ of level $N=N(\Lambda)$. The weight of this
modular form is $nk/2+\sum_{i=1}^k m_k$. This construction generalizes the
theta series $\Theta_\Lambda$ of integral lattices, because $\Theta_\Lambda =
\Theta_{0,\Lambda}$. We give the $q$-expansions of the modular forms
$\Theta_{m,m,\Lambda}$, and $\Theta_{1,1,1,\Lambda}$ and show that (up to some
scaling) they are given by power series with integer coefficients.