  We prove that a non--zero Jacobi form of arbitrary level $N$ and square--free
index $m_1m_2$ with $m_1|N$ and $(N,m_2)=1$ has a non--zero theta component
$h_\mu$ with either $(\mu,2m_1m_2)=1$ or $(\mu,2m_1m_2)\nmid 2m_2$. As an
application, we prove that a non--zero Siegel cusp form $F$ of degree $2$ and
an odd level $N$ in the Atkin--Lehner type newspace is determined by
fundamental Fourier coefficients up to a divisor of $N$.
