The **newform subspace** of a newform $f$ in $S_k^{\rm new}(N,\chi)$ is the subspace generated by $T_p(f)$ for all Hecke operators $T_p$ for $p$ coprime to the level, equivalently, the subspace generated by the Galois conjugates of $f$.

Every newspace has a canonical decomposition into newform subspaces.

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**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2020-01-02 11:44:28

**Referred to by:**

- cmf.dimension
- cmf.galois_orbit
- cmf.heckecharpolys
- lmfdb/classical_modular_forms/templates/cmf_full_gamma1_space.html (line 30)
- lmfdb/classical_modular_forms/templates/cmf_space.html (line 42)
- lmfdb/classical_modular_forms/templates/cmf_space.html (line 174)
- lmfdb/classical_modular_forms/web_newform.py (line 666)
- lmfdb/classical_modular_forms/web_newform.py (line 675)

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