Algebraic modular forms (generally defined by B. Gross) are automorphic forms on algebraic groups whose archimedean part is compact. A part of them is a very classical object such as Brandt matrices for quaternion algebras. They are essentially polynomials invariant by certain finite groups.
Here we talk on two subjects which are closely related with each other.
(1) Comparison of symplectic algebraic modular forms and Siegel modular forms.
(2) Conjectural image of Ihara lifts to symplectic algebraic modular forms.