  We study the elliptic genera of level $N$ at the cusps of $\Gamma_1(N)$ for
any complete intersection. These genera are described as the summations of
generalized binomial coefficients, where each generalized binomial coefficient
is related to the dimension and multi-degree of complete intersection. For
complete intersection $X_n(\underline{d})$, write
$c_1(X_n(\underline{d}))=c_1x$, where $x\in
H^2(X_n(\underline{d});\mathbb{Z})\cong\mathbb{Z}$ is a generator. We mainly
discuss the values of the elliptic genera of level $N$ for $X_n(\underline{d})$
in the case of $c_1>0, =0$ or $<0$. In particular, the values about the Todd
genus, $\hat{A}$-genus and $A_k$-genus of $X_n(\underline{d})$ can be derived
from the elliptic genera of level $N$.
