Geodesic
Symmetric squares of zeta-functions for the principal congruence subgroup of the Siegel group of genus~2
Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 19-36

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Symmetric squares of zeta-functions are introduced for modular forms for the principal congruence subgroup of the integral symplectic group of genus 2. A connection is established between the symmetric squares and Dirichlet series constructed from the Fourier coefficients of modular forms, and an integral representation is obtained. Bibliography: 9 titles. 
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     author = {V. A. Gritsenko},
     title = {Symmetric squares of zeta-functions for the principal congruence subgroup of the {Siegel} group of genus~2},
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     year = {1977},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1977_33_1_a1/}
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V. A. Gritsenko. Symmetric squares of zeta-functions for the principal congruence subgroup of the Siegel group of genus~2. Sbornik. Mathematics, Tome 33 (1977) no. 1, pp. 19-36. http://geodesic.mathdoc.fr/item/SM_1977_33_1_a1/