  In this work, we have analyzed a neutrino model within the distinct framework
of modular forms with degree, $ g>1 $ . This offers a more generalized scenario
of modular forms which is popularly known as Siegel modular forms. We explore
the implications of this special case of automorphic forms for physics beyond
the standard model (BSM) within the lepton sector. In our model, we explicitly
treat the Yukawa couplings as Siegel modular forms with both degree and level
being equivalent to 2. We restrict our modulus parameter for $
\tau_{1}=\tau_{2} $ spanning within the finite modular $ S_{4}\times Z_{2} $
space. This helps us for a broader understanding of the multiplets at higher
degree and simplifies the process of model building of the fermion masses. At
the end, we compute the unknown neutrino oscillation parameters and find the
optimal values of the modulus parameters $ \tau_{1} $ and $ \tau_{3} $ for
which the values of the Yukawa couplings are consistent at $ 3\sigma $ for the
input parameters of neutrinos as given in NuFIT 5.2 and discuss its underlying
physics.
