Space of modular forms of level 336, weight 4, and Character 336.b

• Label: 336.4.b
• Level: $336$
• Weight: $4$
• Character orbit: 336.b
• Rep. character: $\chi_{336}(223,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $6$
• Sturm bound: $256$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(256\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(336, [\chi])\).

	Total	New	Old
Modular forms	204	24	180
Cusp forms	180	24	156
Eisenstein series	24	0	24

Trace form

\( 24 q + 216 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(336, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
336.4.b.a	$336$	$4$	336.b	28.d	$2$	$2$	$2$	$19.825$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(-34\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+\beta q^{5}+(-17-3\beta )q^{7}+9q^{9}+\cdots\)
336.4.b.b	$336$	$4$	336.b	28.d	$2$	$2$	$2$	$19.825$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-6\)	\(0\)	\(28\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}-8\zeta_{6}q^{5}+(14-7\zeta_{6})q^{7}+9q^{9}+\cdots\)
336.4.b.c	$336$	$4$	336.b	28.d	$2$	$2$	$2$	$19.825$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(-28\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}-8\zeta_{6}q^{5}+(-14+7\zeta_{6})q^{7}+\cdots\)
336.4.b.d	$336$	$4$	336.b	28.d	$2$	$2$	$2$	$19.825$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(34\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+\beta q^{5}+(17+3\beta )q^{7}+9q^{9}+\cdots\)
336.4.b.e	$336$	$4$	336.b	28.d	$2$	$8$	$8$	$19.825$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-24\)	\(0\)	\(-4\)	$2^{15}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q-3q^{3}+\beta _{5}q^{5}-\beta _{2}q^{7}+9q^{9}+(-\beta _{1}+\cdots)q^{11}+\cdots\)
336.4.b.f	$336$	$4$	336.b	28.d	$2$	$8$	$8$	$19.825$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(24\)	\(0\)	\(4\)	$2^{15}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+3q^{3}+\beta _{5}q^{5}+\beta _{2}q^{7}+9q^{9}+(\beta _{1}+\cdots)q^{11}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(336, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(336, [\chi]) \cong \)