Siegel modularity of certain Calabi--Yau threefolds over $Q$

We will consider a number of examples of Calabi--Yau threefolds
defined over $Q$ having the Hodge numbers $h^{p,q}=1$ for
all pairs $p,q$ with $p+q=3$. Two of these Calabi--Yau
threefolds are equipped with real multiplication by some
real quadratic fields $K=Q(\sqrt{d})$ with square-free integers
$d>1$, and satisfy the Hilbert modularity over $K$.
Starting with the Hilbert modularity over $K$,
we will establish the Siegel modularity over $Q$
of such Calabi--Yau threefolds that their (cohomological)
$L$-functions coincide with the Andrianov $L$-functions of Siegel
modular forms of weight $3$, genus $2$ on paramodular
subgroups of level $N$ of $Sp(4,Q)$.