179 research outputs found
On the Classification of Lattices Over Which Are Even Unimodular -Lattices of Rank 32
We classify the lattices of rank 16 over the Eisenstein integers which are even unimodular -lattices (of dimension 32). There are exactly 80 unitary isometry classes
Automorphic forms on Feit’s Hermitian lattices
We consider the genus of 20 classes of unimodular Hermitian lattices of rank 12 over the Eisenstein integers. This set is the domain for a certain space of algebraic modular forms. We find a basis of Hecke eigenforms, and guess global Arthur parameters for the associated automorphic representations, which recover the computed Hecke eigenvalues. Congruences between Hecke eigenspaces, combined with the assumed parameters, recover known congruences for classical modular forms, and support new instances of conjectured Eisenstein congruences for U(2,2) automorphic forms
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