Space of modular forms of level 676, weight 6, and Character 676.w

• Label: 676.6.w
• Level: $676$
• Weight: $6$
• Character orbit: 676.w
• Rep. character: $\chi_{676}(7,\cdot)$
• Character field: $\Q(\zeta_{156})$
• Dimension: $21744$
• Sturm bound: $546$

Defining parameters

Level:	\( N \)	\(=\)	\( 676 = 2^{2} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	676.w (of order \(156\) and degree \(48\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 676 \)
Character field:			\(\Q(\zeta_{156})\)
Sturm bound:			\(546\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(676, [\chi])\).

	Total	New	Old
Modular forms	21936	21936	0
Cusp forms	21744	21744	0
Eisenstein series	192	192	0

Trace form

\( 21744 q - 48 q^{2} - 46 q^{4} - 58 q^{5} + 130 q^{6} + 378 q^{8} - 72838 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(676, [\chi])\) into newform subspaces

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