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

• Label: 672.2.b
• Level: $672$
• Weight: $2$
• Character orbit: 672.b
• Rep. character: $\chi_{672}(223,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $2$
• Sturm bound: $256$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(256\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(19\)

Dimensions

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

	Total	New	Old
Modular forms	144	16	128
Cusp forms	112	16	96
Eisenstein series	32	0	32

Trace form

\( 16 q + 16 q^{9} + 8 q^{21} - 32 q^{25} + 16 q^{37} + 32 q^{53} + 16 q^{57} + 32 q^{65} + 64 q^{77} + 16 q^{81} - 112 q^{85} - 32 q^{93}+O(q^{100}) \)

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.b.a	$672$	$2$	672.b	28.d	$2$	$8$	$8$	$5.366$	8.0.836829184.2	None		✓			672.2.b.a	$2$	$0$	\(0\)	\(-8\)	\(0\)	\(-4\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta _{1}q^{5}+\beta _{4}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
672.2.b.b	$672$	$2$	672.b	28.d	$2$	$8$	$8$	$5.366$	8.0.836829184.2	None		✓			672.2.b.a	$2$	$0$	\(0\)	\(8\)	\(0\)	\(4\)	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}-\beta _{1}q^{5}+\beta _{2}q^{7}+q^{9}+(-\beta _{2}+\cdots)q^{11}+\cdots\)

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

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