There is a famous correspondence by Shimura between elliptic modular forms of integral weight and of half-integral weight. What happens when we take Siegel modular forms of level one of degree two? A very concrete conjectural answer on this is a subject of the talk. Also, we give a conjectural congruence between Siegel modular forms of half-integral weight, which corresponds to the one conjectured by Harder for integral weight.