Broué–Enguehard maps and Atkin–Lehner involutions

Let ℓℓ be one of the ten integers such that the sum of their divisors divide 24. For each such ℓℓ, (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 ℓℓ. 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.