  We use Borcherds products to give a new construction of the weight $3$
paramodular nonlift eigenform $f_N$ for levels $N = 61, 73, 79$. We classify
the congruences of $f_N$ to Gritsenko lifts. We provide techniques that compute
eigenvalues to support future modularity applications. Our method does not
compute Hecke eigenvalues from Fourier coefficients but instead uses elliptic
modular forms, specifically the restrictions of Gritsenko lifts and their
images under the slash operator to modular curves.
