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

• Label: 336.2.s
• Level: $336$
• Weight: $2$
• Character orbit: 336.s
• Rep. character: $\chi_{336}(155,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $96$
• Newform subspaces: $4$
• Sturm bound: $128$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 48 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	136	96	40
Cusp forms	120	96	24
Eisenstein series	16	0	16

Trace form

\( 96 q + 12 q^{6} + O(q^{10}) \)

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.s.a	$336$	$2$	336.s	48.k	$4$	$4$	$2$	$2.683$	\(\Q(\zeta_{8})\)	None		$2$	$1$	\(-4\)	\(-4\)	\(-4\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\zeta_{8})q^{2}+(-1+\zeta_{8}^{2})q^{3}-2\zeta_{8}q^{4}+\cdots\)
336.2.s.b	$336$	$2$	336.s	48.k	$4$	$4$	$2$	$2.683$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(4\)	\(0\)	\(4\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\zeta_{8})q^{2}+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+2\zeta_{8}q^{4}+\cdots\)
336.2.s.c	$336$	$2$	336.s	48.k	$4$	$40$	$20$	$2.683$		None		$4$	$0$	\(0\)	\(4\)	\(0\)	\(-40\)		$\mathrm{SU}(2)[C_{4}]$
336.2.s.d	$336$	$2$	336.s	48.k	$4$	$48$	$24$	$2.683$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(48\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 2}\)