  We study a family of Siegel modular forms that are constructed using Jacobi
forms that arise in Umbral moonshine. All but one of them arise as the
Weyl-Kac-Borcherds denominator formula of some Borcherds-Kac-Moody (BKM) Lie
superalgebras. These Lie superalgebras have a $\widehat{sl(2)}$ subalgebra
which we use to study the Siegel modular forms. We show that the expansion of
the Umbral Jacobi forms in terms of $\widehat{sl(2)}$ characters leads to
vector-valued modular forms. We obtain closed formulae for these vector-valued
modular forms. In the Lie algebraic context, the Fourier coefficients of these
vector-valued modular forms are related to multiplicities of roots appearing on
the sum side of the Weyl-Kac-Borcherds denominator formulae.
