Construction of cusp forms using Rankin-Cohen brackets

For a fix modular form g and a non negative ineteger ν, by using Rankin-Cohen bracket we first define a linear map $T_{g,ν}$ on the space of modular forms. We explicitly compute the adjoint of this map and show that the n-th Fourier coefficients of the image of the cusp form f under this map is, upto a constant a special value of Rankin-Selberg convolution of f and g.

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