Taille des valeurs de fonctions L de carrés symétriques au bord de la bande critique

For each weight k and level N square free and without small prime factors, we prove the existence of primitive forms f_+ and f_- of weight k and level N such that L(1,sym^2f_+)ₖ[loglog(3N)]³ and L(1,sym^2f_-)ₖ[loglog(3N)]⁻¹. The result comes from a delicate study of the moments of L(1,sym^2 f) . This study gives also results for squarefree levels but with small prime factors. It provides counterexamples to the equivalence between harmonic and natural means.