Space of modular forms of level 315, weight 10, and Character 315.bb

• Label: 315.10.bb
• Level: $315$
• Weight: $10$
• Character orbit: 315.bb
• Rep. character: $\chi_{315}(89,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $288$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(480\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(315, [\chi])\).

	Total	New	Old
Modular forms	880	288	592
Cusp forms	848	288	560
Eisenstein series	32	0	32

Trace form

\( 288 q - 36864 q^{4} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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

Decomposition of \(S_{10}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)