Space of modular forms of level 693, weight 6, and Character 693.bj

• Label: 693.6.bj
• Level: $693$
• Weight: $6$
• Character orbit: 693.bj
• Rep. character: $\chi_{693}(76,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $952$
• Sturm bound: $576$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	693.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 693 \)
Character field:			\(\Q(\zeta_{6})\)
Sturm bound:			\(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(693, [\chi])\).

	Total	New	Old
Modular forms	968	968	0
Cusp forms	952	952	0
Eisenstein series	16	16	0

Trace form

\( 952 q + 7548 q^{4} + 432 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

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