Space of modular forms of level 336, weight 2, and Character 336.bq

• Label: 336.2.bq
• Level: $336$
• Weight: $2$
• Character orbit: 336.bq
• Rep. character: $\chi_{336}(37,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $128$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.bq (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(128\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(336, [\chi])\).

	Total	New	Old
Modular forms	272	128	144
Cusp forms	240	128	112
Eisenstein series	32	0	32

Trace form

\( 128 q + 4 q^{4} + 24 q^{8} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(336, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
336.2.bq.a	$336$	$2$	336.bq	112.w	$12$	$8$	$2$	$2.683$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{12}]$	\(q+(\zeta_{24}-\zeta_{24}^{7})q^{2}+\zeta_{24}^{5}q^{3}+(2-2\zeta_{24}^{4}+\cdots)q^{4}+\cdots\)
336.2.bq.b	$336$	$2$	336.bq	112.w	$12$	$120$	$30$	$2.683$		None		$4$	$0$	\(0\)	\(0\)	\(-8\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$

Decomposition of \(S_{2}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(336, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 2}\)