Summary: Let \((A,\mathscr{L},\Theta_n)\) be a dimension \(g\) abelian variety together with a level \(n\) theta structure over a field \(k\) of odd characteristic. We thus denote by \((\theta^{\Theta_{\mathscr{L}}}_i)_{(\mathbb{Z}/n \mathbb{Z})^g}\in\Gamma (A,\mathscr{L})\) the associated standard basis. For a positive integer \(\ell\) relatively prime to \(n\) and the characteristic of \(k\), we study change of level algorithms which allow one to compute level \(\ell n\) theta functions \((\theta_i^{\Theta_{\mathscr{L}^\ell}}(x))_{i\in (\mathbb{Z}/\ell n\mathbb{Z})^g}\) from the knowledge of level \(n\) theta functions \((\theta^{\Theta_{\mathscr{L}}}_i(x))_{(\mathbb{Z}/n \mathbb{Z})^g}\) or vice versa. The classical duplication formulas are an example of change of level algorithm to go from level \(n\) to level \(2n\). The main result of this paper states that there exists an algorithm to go from level \(n\) to level \(\ell n\) in \(O(n^g \ell^{2g})\) operations in \(k\). We derive an algorithm to compute an isogeny \(f:A\rightarrow B\) from the knowledge of \((A,\mathscr{L},\Theta_n)\) and \(K\subset A[\ell]\) isotropic for the Weil pairing which computes \(f(x)\) for \(x\in A(k)\) in \(O((n\ell)^g)\) operations in \(k\). We remark that this isogeny computation algorithm is of quasi-linear complexity in the size of \(K\).