Hermitian modular forms congruent to 1 modulo p

Abstract

For any natural number ℓ and any prime p ≡ 1 (mod 4) not dividing ℓ there is a Hermitian modular form of arbitrary genus n over L := Q[ √ −ℓ] that is congruent to 1 modulo p which is a Hermitian theta series of an O L -lattice of rank p − 1 admitting a fixed point free automorphism of order p. It is shown that also for non-free lattices such theta series are modular forms.