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

• Label: 336.2.b
• Level: $336$
• Weight: $2$
• Character orbit: 336.b
• Rep. character: $\chi_{336}(223,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $4$
• Sturm bound: $128$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(128\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	76	8	68
Cusp forms	52	8	44
Eisenstein series	24	0	24

Trace form

\( 8 q + 8 q^{9} + O(q^{10}) \)

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.b.a	$336$	$2$	336.b	28.d	$2$	$2$	$2$	$2.683$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+(-2-\zeta_{6})q^{7}+q^{9}-2\zeta_{6}q^{11}+\cdots\)
336.2.b.b	$336$	$2$	336.b	28.d	$2$	$2$	$2$	$2.683$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(-2\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-q^{3}+\beta q^{5}+(1-\beta )q^{7}+q^{9}+\beta q^{11}+\cdots\)
336.2.b.c	$336$	$2$	336.b	28.d	$2$	$2$	$2$	$2.683$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+\beta q^{5}+(-1+\beta )q^{7}+q^{9}-\beta q^{11}+\cdots\)
336.2.b.d	$336$	$2$	336.b	28.d	$2$	$2$	$2$	$2.683$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(2\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+q^{3}+(2+\zeta_{6})q^{7}+q^{9}+2\zeta_{6}q^{11}+\cdots\)

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

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