  The new era of multimessenger astrophysics requires the capability of
studying different aspects of the evolution of compact objects. In particular,
the merger of neutron star binaries is a strong source of gravitational waves
and electromagnetic radiation, from radio to $\gamma$-rays, as demonstrated by
the detection of GW170817 and its electromagnetic counterparts. In order to
understand the physical mechanisms involved in such systems, it is necessary to
employ fully general relativistic magnetohydrodynamic (GRMHD) simulations able
to include the effects of a composition and temperature dependent equation of
state describing neutron star matter as well as neutrino emission and
reabsorption. Here, we present our new code named $\texttt{Spritz}$ that solves
the GRMHD equations in 3D Cartesian coordinates and on a dynamical spacetime.
The code can support tabulated equations of state, taking into account finite
temperature effects and allowing for the inclusion of neutrino radiation. In
this first paper, we present the general features of the code and a series of
tests performed in special and general relativity to assess the robustness of
the basic GRMHD algorithms implemented. Among these tests, we also present the
first comparison between a non-staggered and a staggered formulation of the
vector potential evolution, which is used to guarantee the divergence-less
character of the magnetic field. With respect to other publicly available GRMHD
codes, $\texttt{Spritz}$ combines the robust approach of a staggered
formulation of the vector potential together with the use of an equation of
state driver ($\texttt{EOS_Omni}$) that can allow the code to use finite
temperature equations of state. A next version of the code will fully test the
$\texttt{EOS_Omni}$ driver by coupling it with a neutrino leakage scheme.
