Space of modular forms of level 672, weight 2, and Character 672.cf

• Label: 672.2.cf
• Level: $672$
• Weight: $2$
• Character orbit: 672.cf
• Rep. character: $\chi_{672}(19,\cdot)$
• Character field: $\Q(\zeta_{24})$
• Dimension: $512$
• Newform subspaces: $1$
• Sturm bound: $256$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	672.cf (of order \(24\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 224 \)
Character field:			\(\Q(\zeta_{24})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(256\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(672, [\chi])\).

	Total	New	Old
Modular forms	1056	512	544
Cusp forms	992	512	480
Eisenstein series	64	0	64

Trace form

512 * q + 64 * q^14 + 8 * q^16 - 8 * q^18 - 16 * q^22 - 16 * q^23 - 40 * q^28 + 48 * q^35 + 32 * q^43 + 8 * q^44 + 48 * q^50 - 72 * q^52 + 32 * q^53 + 32 * q^58 - 192 * q^59 - 48 * q^60 + 144 * q^64 - 144 * q^66 - 16 * q^67 - 72 * q^70 + 128 * q^71 + 32 * q^74 + 48 * q^78 - 72 * q^80 - 120 * q^82 + 88 * q^88 - 48 * q^91 + 128 * q^92 - 72 * q^94 - 120 * q^96 - 136 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(672, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
672.2.cf.a	$672$	$2$	672.cf	224.ae	$24$	$512$	$64$	$5.366$		None		✓	✓	✓	672.2.cf.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{24}]$

Decomposition of \(S_{2}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(672, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(224, [\chi])\)\(^{\oplus 2}\)