Geodesic
Modular forms and Hilbert functions for the field $Q(\sqrt 2)$
Matematičeskie zametki, Tome 4 (1968) no. 2, pp. 129-136.

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A new proof is given of Hammond's result on the algebraic structure of the graduated ring of integral modular forms of even weight relative to the Hilbert modular group $\Gamma$ for the field $Q(\sqrt2)$. The algebraic structure is also found of the field of all modular Hilbert functions relative to $\Gamma$. 
@article{MZM_1968_4_2_a1,
     author = {O. M. Fomenko},
     title = {Modular forms and {Hilbert} functions for the field $Q(\sqrt 2)$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {129--136},
     publisher = {mathdoc},
     volume = {4},
     number = {2},
     year = {1968},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a1/}
}
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O. M. Fomenko. Modular forms and Hilbert functions for the field $Q(\sqrt 2)$. Matematičeskie zametki, Tome 4 (1968) no. 2, pp. 129-136. http://geodesic.mathdoc.fr/item/MZM_1968_4_2_a1/