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

• Label: 672.4.j
• Level: $672$
• Weight: $4$
• Character orbit: 672.j
• Rep. character: $\chi_{672}(239,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $512$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.j (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 24 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(512\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	400	72	328
Cusp forms	368	72	296
Eisenstein series	32	0	32

Trace form

\( 72 q + O(q^{10}) \)

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.j.a	$672$	$4$	672.j	24.f	$2$	$72$	$72$	$39.649$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

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

\( S_{4}^{\mathrm{old}}(672, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)