Space of modular forms of level 336, weight 3, and Character 336.v

• Label: 336.3.v
• Level: $336$
• Weight: $3$
• Character orbit: 336.v
• Rep. character: $\chi_{336}(83,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $248$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	336.v (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 336 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(336, [\chi])\).

	Total	New	Old
Modular forms	264	264	0
Cusp forms	248	248	0
Eisenstein series	16	16	0

Trace form

\( 248 q - 8 q^{4} - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(336, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
336.3.v.a	$336$	$3$	336.v	336.v	$4$	$248$	$124$	$9.155$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$