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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).

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