Abstract : We give four contributions to the study of $L$-functions of modular forms. First, we prove that the Jacobian of a modular curve has a simple quotient of great dimension and rank $0$ and a simple quotient of great dimension and great rank. In a second contribution we prove the $1$-level density conjecture for new families of modular $L$-functions. Then, we study the distribution of the value at $1$ of the $L$-function of the symetric square of a modular form. Finally, we give, in collaboration with F. Martin, a criteria for the determination of modular forms by the special values of their $L$-functions.