For $g=8,12,16$ and $24$, there is a nonzero alternating $g$-multilinear form on the ${\\rm Leech}$ lattice, unique up to a scalar, which is invariant by the orthogonal group of ${\\rm Leech}$. The harmonic Siegel theta series built from these alternating forms are Siegel modular cuspforms of weight $13$ for ${\\rm Sp}{2g}(\\mathbb{Z})$. We prove that they are nonzero eigenforms, determine one of their Fourier coefficients, and give informations about their standard ${\\rm L}$-functions. These forms are interesting since, by a recent work of the authors, they are the only nonzero Siegel modular forms of weight $13$ for ${\\rm Sp}{2n}(\\mathbb{Z})$, for any $n\\geq 1$.