Space of modular forms of level 825, weight 4, and Character 825.cb

• Label: 825.4.cb
• Level: $825$
• Weight: $4$
• Character orbit: 825.cb
• Rep. character: $\chi_{825}(169,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $720$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	825.cb (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 275 \)
Character field:			\(\Q(\zeta_{10})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(825, [\chi])\).

	Total	New	Old
Modular forms	1456	720	736
Cusp forms	1424	720	704
Eisenstein series	32	0	32

Trace form

\( 720 q + 720 q^{4} - 24 q^{5} + 96 q^{6} - 30 q^{7} + 1620 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(825, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{4}^{\mathrm{old}}(825, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(825, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(275, [\chi])\)\(^{\oplus 2}\)