Geodesic
Applications of the Petersson formula for a bilinear form in Fourier coefficients of cusp forms
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 11, Tome 204 (1993), pp. 143-166 
O. M. Fomenko. Applications of the Petersson formula for a bilinear form in Fourier coefficients of cusp forms. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 11, Tome 204 (1993), pp. 143-166. http://geodesic.mathdoc.fr/item/ZNSL_1993_204_a9/
@article{ZNSL_1993_204_a9,
     author = {O. M. Fomenko},
     title = {Applications of the {Petersson} formula for a~bilinear form in {Fourier} coefficients of cusp forms},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {143--166},
     year = {1993},
     volume = {204},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1993_204_a9/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

Let $S_{2k}(\Gamma_0(N),\chi)$ be the space of holomorphic $\Gamma_0(N)$-cusp forms of integral weight $k$ and character $\chi$. Let $f_j(z)$, $1\le j\le v_{2k}^\mathrm{new}(p)$, be the set of normalized newforms of $S_{2k}(\Gamma_0(p),1)$, where $p$ is a prime, and let $L_j(s)=L_{f_j}(s)$ be the $L$-function of $f_j(z)$. It is proved that $$ \sum_{1\le j\le v_{2k}^\mathrm{new}(p)}L_j^2\left(\frac12\right)\ll p\log^4p\cdot\log\log p,\qquad p\to\infty, $$ where $2k\ge4$. Errors in an earlier paper (RŽMat, 1989, 4A65) are corrected. Bibliography: 11 titles.