Broué–Enguehard maps and Atkin–Lehner involutions

Let ℓ be one of the ten integers such that the sum of their divisors divide 24. For each such ℓ , (except 15) we give a map from an algebra of polynomial invariants of some finite group to the algebra of modular forms invariant under the Atkin–Lehner group of level ℓ . These maps are motivated and inspired by constructions of modular lattices from self-dual codes over rings. This work generalizes Broué–Enguehard work in level one and three obtained from binary and ternary codes.