p-adic Siegel–Eisenstein series of degree two

We prove an explicit formula for Fourier coefficients of Siegel–Eisenstein series of degree two with a primitive character of any conductor. Moreover, we prove that there exists the p-adic analytic family which consists of Siegel–Eisenstein series of degree two and a certain p-adic limit of Siegel–Eisenstein series of degree two is actually a Siegel–Eisenstein series of degree two.