Ikeda lift

In mathematics, the Ikeda lift is a lifting of modular forms to Siegel modular forms.

It generalized the Saito–Kurokawa lift from modular forms of weight 2k to genus 2 Siegel modular forms of weight k + 1.

Suppose that k and n are positive integers of the same parity.

The Ikeda lift takes a Hecke eigenform of weight 2k for SL2(Z) to a Hecke eigenform in the space of Siegel modular forms of weight k+n, degree 2n.

The Ikeda lift takes the Delta function (the weight 12 cusp form for SL2(Z)) to the Schottky form, a weight 8 Siegel cusp form of degree 4.