Geodesic
Theta-series of even unimodular 24-dimensional lattices
Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 82-93

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It is proved that the twelve theta-series of the even unimodular 24-dimensional lattices are linearly independent and one finds all the relations among the $k$-th theta-series of these lattices for $k\leqslant4$. 
@article{ZNSL_1979_86_a8,
     author = {V. A. Erokhin},
     title = {Theta-series of even unimodular 24-dimensional lattices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {82--93},
     publisher = {mathdoc},
     volume = {86},
     year = {1979},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a8/}
}
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V. A. Erokhin. Theta-series of even unimodular 24-dimensional lattices. Zapiski Nauchnykh Seminarov POMI, Algebraic numbers and finite groups, Tome 86 (1979), pp. 82-93. http://geodesic.mathdoc.fr/item/ZNSL_1979_86_a8/