The **dimension** of a space of modular forms is its dimension as a complex vector space; for spaces of newforms $S_k^{\rm new}(N,\chi)$ this is the same as the dimension of the $\Q$-vector space spanned by its eigenforms.

The **dimension** of a newform refers to the dimension of the $\Q$-vector space spanned by its Galois conjugates, equivalently, its orbit under the Hecke operators. This is equal to the degree of its coefficient field (as an extension of $\Q$).

The **relative dimension** of $S_k^{\rm new}(N,\chi)$ is its dimension as a $\Q(\chi)$-vector space, where $\Q(\chi)$ is the field generated by the values of $\chi$, and similarly for newforms $f\in S_k^{\rm new}(N,\chi)$.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2019-01-30 16:01:38

**Referred to by:**

- cmf.display_dim
- cmf.galois_conjugate
- cmf.hecke_kernels
- cmf.inner_twist_count
- cmf.trace_bound
- cmf.trace_form
- rcs.cande.cmf
- rcs.cande.lfunction
- rcs.rigor.cmf
- rcs.source.cmf
- lmfdb/classical_modular_forms/main.py (lines 1163-1164)
- lmfdb/classical_modular_forms/templates/cmf_browse.html (line 158)
- lmfdb/classical_modular_forms/templates/cmf_newform_common.html (line 51)
- lmfdb/classical_modular_forms/templates/cmf_refine_search.html (line 53)
- lmfdb/classical_modular_forms/templates/cmf_space_refine_search.html (line 38)
- lmfdb/classical_modular_forms/templates/cmf_trace_display.html (line 6)

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

- 2019-01-30 16:01:38 by Andrew Sutherland (Reviewed)