  Various forms of spin and charge ordering have been identified in a wide
range of cuprate superconducting materials, but whether these behaviors are
ubiquitous phenomena is not established. In this work we focus on one of the
simplest compounds, HgBa$_{2}$CuO$_{4+\delta}$ (Hg1201), a superconductor with
a high transition temperature, 97 K, having only a single layer and tetragonal
structure, in contrast to one of the most extensively studied materials,
YBa$_{2}$Cu$_{3}$O$_{6+y}$ (Y123). Using nuclear magnetic resonance we have
discovered a coherent spatial modulation of both spin and charge that is
temperature and magnetic field independent, in competition with
superconductivity similar to other cuprates. However, there is no evidence for
the magnetic field and temperature induced charge order observed in Y123.
Electronic instabilities are a common feature of cuprates as in the present
work on Hg1201, but their manifestations are not universal.
