Conway invariant Jacobi forms on the Leech lattice

Abstract In this paper, we study Jacobi forms associated with the Leech lattice Λ which are invariant under Conway group Co 0 {\operatorname{Co}_{0}} . We determine and construct generators of modules both weak holomorphic integral weight fixed index t ≤ 3 {t\leq 3} As applications, (i) find modular linear differential equations satisfied by generators; (ii) decompositions many products orbits vectors; (iii) calculate intersections between (iv) derive some conjugate relations among modulo ⁢ Λ {t\Lambda}