Space of modular forms of level 693, weight 2, and Character 693.db

• Label: 693.2.db
• Level: $693$
• Weight: $2$
• Character orbit: 693.db
• Rep. character: $\chi_{693}(5,\cdot)$
• Character field: $\Q(\zeta_{30})$
• Dimension: $736$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.db (of order \(30\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 693 \)
Character field:			\(\Q(\zeta_{30})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(693, [\chi])\).

	Total	New	Old
Modular forms	800	800	0
Cusp forms	736	736	0
Eisenstein series	64	64	0

Trace form

\( 736 q - 9 q^{3} + 170 q^{4} - 9 q^{5} - 12 q^{6} - 3 q^{7} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(693, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
693.2.db.a	$693$	$2$	693.db	693.cb	$30$	$736$	$92$	$5.534$		None		$4$	$0$	\(0\)	\(-9\)	\(-9\)	\(-3\)		$\mathrm{SU}(2)[C_{30}]$