Space of modular forms of level 630, weight 2, and Character 630.bt

• Label: 630.2.bt
• Level: $630$
• Weight: $2$
• Character orbit: 630.bt
• Rep. character: $\chi_{630}(317,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $192$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	630.bt (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 315 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(630, [\chi])\).

	Total	New	Old
Modular forms	608	192	416
Cusp forms	544	192	352
Eisenstein series	64	0	64

Trace form

\( 192 q + 8 q^{6} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(630, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
630.2.bt.a	$630$	$2$	630.bt	315.ax	$12$	$192$	$48$	$5.031$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(630, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(630, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(315, [\chi])\)\(^{\oplus 2}\)