Space of modular forms of level 684, weight 5, and Character 684.b

• Label: 684.5.b
• Level: $684$
• Weight: $5$
• Character orbit: 684.b
• Rep. character: $\chi_{684}(683,\cdot)$
• Character field: $\Q$
• Dimension: $160$
• Sturm bound: $600$

Defining parameters

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	684.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 228 \)
Character field:			\(\Q\)
Sturm bound:			\(600\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(684, [\chi])\).

	Total	New	Old
Modular forms	488	160	328
Cusp forms	472	160	312
Eisenstein series	16	0	16

Trace form

\( 160 q + 56 q^{4} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(684, [\chi])\) into newform subspaces

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

Decomposition of \(S_{5}^{\mathrm{old}}(684, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(684, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(228, [\chi])\)\(^{\oplus 2}\)