  This paper studies the Fourier expansion of Hecke-Maass eigenforms for $GL(2,
\mathbb Q)$ of arbitrary weight, level, and character at various cusps.
Translating well known results in the theory of adelic automorphic
representations into classical language, a multiplicative expression for the
Fourier coefficients at any cusp is derived. In general, this expression
involves Fourier coefficients at several different cusps. A sufficient
condition for the existence of multiplicative relations among Fourier
coefficients at a single cusp is given. It is shown that if the level is 4
times (or in some cases 8 times) an odd squarefree number then there are
multiplicative relations at every cusp. We also show that a local
representation of $GL(2, \mathbb Q_p)$ which is isomorphic to a local factor of
a global cuspidal automorphic representation generated by the adelic lift of a
newform of arbitrary weight, level $N$, and character $\chi\pmod{N}$ cannot be
supercuspidal if $\chi$ is primitive. Furthermore, it is supercuspidal if and
only if at every cusp (of width $m$ and cusp parameter = 0) the $mp^\ell$
Fourier coefficient, at that cusp, vanishes for all sufficiently large positive
integers $\ell$. In the last part of this paper a three term identity involving
the Fourier expansion at three different cusps is derived.
