Space of modular forms of level 672, weight 4, and Character 672.bl

• Label: 672.4.bl
• Level: $672$
• Weight: $4$
• Character orbit: 672.bl
• Rep. character: $\chi_{672}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $512$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.bl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(512\)
Trace bound:			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(672, [\chi])\).

	Total	New	Old
Modular forms	800	96	704
Cusp forms	736	96	640
Eisenstein series	64	0	64

Trace form

\( 96 q - 432 q^{9} + 240 q^{21} + 1368 q^{25} - 72 q^{33} + 504 q^{37} - 368 q^{49} - 784 q^{53} + 336 q^{57} - 1200 q^{61} + 560 q^{65} + 648 q^{73} + 3136 q^{77} - 3888 q^{81} - 2112 q^{85} - 2760 q^{93}+O(q^{100}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(672, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
672.4.bl.a	$672$	$4$	672.bl	28.f	$6$	$48$	$24$	$39.649$		None		✓			672.4.bl.a	$2$	$0$	\(0\)	\(-72\)	\(0\)	\(-20\)		$\mathrm{SU}(2)[C_{6}]$
672.4.bl.b	$672$	$4$	672.bl	28.f	$6$	$48$	$24$	$39.649$		None		✓			672.4.bl.a	$2$	$0$	\(0\)	\(72\)	\(0\)	\(20\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(672, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)