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

• Label: 672.4.c
• Level: $672$
• Weight: $4$
• Character orbit: 672.c
• Rep. character: $\chi_{672}(337,\cdot)$
• Character field: $\Q$
• Dimension: $36$
• Newform subspaces: $2$
• Sturm bound: $512$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(512\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	400	36	364
Cusp forms	368	36	332
Eisenstein series	32	0	32

Trace form

\( 36 q + 28 q^{7} - 324 q^{9} + O(q^{10}) \)

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.c.a	$672$	$4$	672.c	8.b	$2$	$16$	$16$	$39.649$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-112\)	$2^{38}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{3}-\beta _{2}q^{5}-7q^{7}-9q^{9}+(-3\beta _{5}+\cdots)q^{11}+\cdots\)
672.4.c.b	$672$	$4$	672.c	8.b	$2$	$20$	$20$	$39.649$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(140\)	$2^{60}\cdot 3^{10}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}-\beta _{1}q^{5}+7q^{7}-9q^{9}+(-2\beta _{2}+\cdots)q^{11}+\cdots\)

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

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