  We give more evidence for Patterson's conjecture on sums of exponential sums,
by getting an asymptotic for a sum of quartic exponential sums over $\Q[i].$
Previously, the strongest evidence of Patterson's conjecture over a number
field is the paper of Livn\'{e} and Patterson \cite{LP} on sums of cubic
exponential sums over $\Q[\omega], \omega^3=1.$
  The key ideas in getting such an asymptotic are a Kuznetsov-like trace
formula for metaplectic forms over a quartic cover of $GL_2,$ and an identity
on exponential sums relating Kloosterman sums and quartic exponential sums. To
synthesize the spectral theory and the exponential sum identity, there is need
for a good amount of analytic number theory.
  An unexpected aspect of the asymptotic of the sums of exponential sums is
that there can be a secondary main term additional to the main term which is
not predicted in Patterson's original paper \cite{P}.
