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

• Label: 315.10.bv
• Level: $315$
• Weight: $10$
• Character orbit: 315.bv
• Rep. character: $\chi_{315}(23,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $1712$
• Sturm bound: $480$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	315.bv (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Sturm bound:			\(480\)

Dimensions

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

	Total	New	Old
Modular forms	1744	1744	0
Cusp forms	1712	1712	0
Eisenstein series	32	32	0

Trace form

\( 1712 q - 2 q^{3} - 6 q^{5} + 9072 q^{6} - 2 q^{7} + O(q^{10}) \)

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

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