Elliptic functions

The Weierstrass $\wp$-function is given by $$ \wp(z,\tau)=\frac{1}{z^{2}}+\sum_{(k,l)\neq (0,0)}\left(\frac{1}{(z-(k\tau+l))^{2}}-\frac{1}{(k\tau+l)^{2}}\right). $$ Let $\lambda$ be primitive $n$th root of unity. One can define another elliptic function \begin{align}\displaystyle \sum_{k=0}^{n-1}\lambda^{k}\wp(z+k\tau,n\tau).\end{align} Since every elliptic function can be expressed as rational function in terms of $\wp$ and its derivative $\wp'$, in this case, I was wondering if it is possible to write it in terms of $\wp(z,n\tau)$ and $\wp'(z,n\tau)$ explicitly, or can it be identified with some familiar elliptic funtion, or is there some modularity property with respect to some congruence subgroup of $SL_{2}(\mathbb{Z})$? Any suggestion or references would be appreciated.