Action of the irregular Hecke operator for a prime number p on the theta series of a quadratic form

Let $F$ be a positive-definite integral even matrix of even order. For an arbitrary prime number $p$ and natural $n$ one obtains an explicit expression for the image of the theta series of genus $n$ of the matrix $F$, under the action of an irregular Hecke operator with index $p$, in the form of a linear combination of theta series.