Space of modular forms of level 672, weight 3, and Character 672.o

• Label: 672.3.o
• Level: $672$
• Weight: $3$
• Character orbit: 672.o
• Rep. character: $\chi_{672}(671,\cdot)$
• Character field: $\Q$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	672.o (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(672, [\chi])\).

	Total	New	Old
Modular forms	272	64	208
Cusp forms	240	64	176
Eisenstein series	32	0	32

Trace form

\( 64 q - 16 q^{21} + 352 q^{25} + 160 q^{37} - 64 q^{49} + 32 q^{57} + 256 q^{81} + 32 q^{85} + 320 q^{93}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(672, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
672.3.o.a	$672$	$3$	672.o	84.h	$2$	$32$	$32$	$18.311$		None		✓			672.3.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$
672.3.o.b	$672$	$3$	672.o	84.h	$2$	$32$	$32$	$18.311$		None		✓			672.3.o.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{3}^{\mathrm{old}}(672, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(672, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)