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

• Label: 672.4.b
• Level: $672$
• Weight: $4$
• Character orbit: 672.b
• Rep. character: $\chi_{672}(223,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
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	400	48	352
Cusp forms	368	48	320
Eisenstein series	32	0	32

Trace form

\( 48 q + 432 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
672.4.b.a	$672$	$4$	672.b	28.d	$2$	$24$	$24$	$39.649$		None		$2$	$0$	\(0\)	\(-72\)	\(0\)	\(-20\)		$\mathrm{SU}(2)[C_{2}]$
672.4.b.b	$672$	$4$	672.b	28.d	$2$	$24$	$24$	$39.649$		None		$2$	$0$	\(0\)	\(72\)	\(0\)	\(20\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{4}^{\mathrm{old}}(672, [\chi]) \cong \)