Space of modular forms of level 968, weight 2, and Character 968.bd

• Label: 968.2.bd
• Level: $968$
• Weight: $2$
• Character orbit: 968.bd
• Rep. character: $\chi_{968}(5,\cdot)$
• Character field: $\Q(\zeta_{110})$
• Dimension: $5200$
• Newform subspaces: $1$
• Sturm bound: $264$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 968 = 2^{3} \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	968.bd (of order \(110\) and degree \(40\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 968 \)
Character field:			\(\Q(\zeta_{110})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(264\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(968, [\chi])\).

	Total	New	Old
Modular forms	5360	5360	0
Cusp forms	5200	5200	0
Eisenstein series	160	160	0

Trace form

\( 5200 q - 39 q^{2} - 43 q^{4} - 59 q^{6} - 78 q^{7} - 39 q^{8} + 1200 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(968, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
968.2.bd.a	$968$	$2$	968.bd	968.ad	$110$	$5200$	$130$	$7.730$		None		✓	968.2.bd.a	$4$	$0$	\(-39\)	\(0\)	\(0\)	\(-78\)		$\mathrm{SU}(2)[C_{110}]$