A finite Smith–Toda complex V(4) at the prime 1009

We construct a Smith–Toda complex $V(4)$ at the prime 1009. It is an ordinary finite 1009-local spectrum whose Brown–Peterson homology is $B{P}_{\ast }/(1009,v_1,v_2,v_3,v_4)$, with its canonical comodule structure and generator in degree zero.