Space of modular forms of level 315, weight 4, and Character 315.z

• Label: 315.4.z
• Level: $315$
• Weight: $4$
• Character orbit: 315.z
• Rep. character: $\chi_{315}(104,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $280$
• Sturm bound: $192$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.z (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(192\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

	Total	New	Old
Modular forms	296	296	0
Cusp forms	280	280	0
Eisenstein series	16	16	0

Trace form

\( 280 q - 548 q^{4} - 12 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) into newform subspaces

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