Geodesic
Eichler--Shimura cohomology in the case of Siegel modular forms
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 128-135

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One generalizes the Eichler–Shimura result, connecting the space of parabolic modular forms relative to a group $\Gamma$ with the cohomologies of the group $\Gamma$, to the case of the Siegel modular forms. 
@article{ZNSL_1985_144_a11,
     author = {A. Yu. Nenashev},
     title = {Eichler--Shimura cohomology in the case of {Siegel} modular forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {128--135},
     publisher = {mathdoc},
     volume = {144},
     year = {1985},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_144_a11/}
}
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A. Yu. Nenashev. Eichler--Shimura cohomology in the case of Siegel modular forms. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 6, Tome 144 (1985), pp. 128-135. http://geodesic.mathdoc.fr/item/ZNSL_1985_144_a11/