The new part of the space $S_k(N,\chi)$ of cusp forms of weight $k$, level $N$, and character $\chi$ is the space of $S_k^{\rm new}(N,\chi)$ of newforms.

It can be decomposed into irreducible subspaces under the action of the Hecke operators, each of which corresponds to a Galois orbit of newforms (the absolute Galois group of $\Q$ acts the set of newforms in $S_k^{\rm new}(N,\chi)$ via its action on the coefficients of $q$-expansions).

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2018-10-06 11:32:40

**Referred to by:**

**History:**(expand/hide all)

- 2018-10-06 11:32:40 by Andrew Sutherland (Reviewed)