  We revisit the topic of the mean field ground state of a spin-1 atomic
condensate inside a uniform magnetic field ($B$) under the constraints that
both the total number of atoms ($N$) and the magnetization ($\cal M$) are
conserved. In the presence of an internal state (spin component) independent
trap, we also investigate the dependence of the so-called single spatial mode
approximation (SMA) on the magnitude of the magnetic field and ${\cal M}$. Our
result indicate that the quadratic Zeeman effect is an important factor in
balancing the mean field energy from elastic atom-atom collisions that are
known to conserve both $N$ and $\cal M$.
