  We study a new orthogonal family of $L$-functions associated with holomorphic
Hecke newforms of level $q$, averaged over $q \asymp Q$. To illustrate our
methods, we prove a one level density result for this family with the support
of the Fourier transform of the test function being extended to be inside $(-4,
4)$. The main techniques developed in this paper will be useful in developing
further results for this family, including estimates for high moments,
information on the vertical distribution of zeros, as well as critical line
theorems.
