Geodesic
Action of the irregular Hecke operator for a prime number p on the theta series of a quadratic form
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 68-71 
S. A. Evdokimov. Action of the irregular Hecke operator for a prime number p on the theta series of a quadratic form. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 68-71. http://geodesic.mathdoc.fr/item/ZNSL_1985_144_a6/
@article{ZNSL_1985_144_a6,
     author = {S. A. Evdokimov},
     title = {Action of the irregular {Hecke} operator for a prime number p on the theta series of a quadratic form},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {68--71},
     year = {1985},
     volume = {144},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_144_a6/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.