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Abstract

In this paper we study Jacobi forms associated with the Leech lattice
$\Lambda$ which are invariant under the Conway group $\mathrm{Co}_0$. We
determine and construct generators of modules of both weak and holomorphic
Jacobi forms of integral weight and fixed index $t\leq 3$. As applications, (1)
we find the modular linear differential equations satisfied by the holomorphic
generators; (2) we determine the decomposition of many products of orbits of
Leech vectors; (3) we calculate the intersection between orbits and Leech
vectors; (4) we derive some conjugate relations among orbits modulo $t\Lambda$.