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

• Label: 336.4.bj
• Level: $336$
• Weight: $4$
• Character orbit: 336.bj
• Rep. character: $\chi_{336}(95,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $7$
• Sturm bound: $256$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.bj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(256\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(13\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	408	96	312
Cusp forms	360	96	264
Eisenstein series	48	0	48

Trace form

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

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.bj.a	$336$	$4$	336.bj	84.n	$6$	$2$	$1$	$19.825$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-9\)	\(0\)	\(17\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-6+3\zeta_{6})q^{3}+(-1+19\zeta_{6})q^{7}+\cdots\)
336.4.bj.b	$336$	$4$	336.bj	84.n	$6$	$2$	$1$	$19.825$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-9\)	\(0\)	\(37\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-6+3\zeta_{6})q^{3}+(19-\zeta_{6})q^{7}+(3^{3}+\cdots)q^{9}+\cdots\)
336.4.bj.c	$336$	$4$	336.bj	84.n	$6$	$2$	$1$	$19.825$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(9\)	\(0\)	\(-37\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(6-3\zeta_{6})q^{3}+(-19+\zeta_{6})q^{7}+(3^{3}+\cdots)q^{9}+\cdots\)
336.4.bj.d	$336$	$4$	336.bj	84.n	$6$	$2$	$1$	$19.825$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(9\)	\(0\)	\(-17\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(6-3\zeta_{6})q^{3}+(1-19\zeta_{6})q^{7}+(3^{3}+\cdots)q^{9}+\cdots\)
336.4.bj.e	$336$	$4$	336.bj	84.n	$6$	$28$	$14$	$19.825$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-38\)		$\mathrm{SU}(2)[C_{6}]$
336.4.bj.f	$336$	$4$	336.bj	84.n	$6$	$28$	$14$	$19.825$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(38\)		$\mathrm{SU}(2)[C_{6}]$
336.4.bj.g	$336$	$4$	336.bj	84.n	$6$	$32$	$16$	$19.825$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{4}^{\mathrm{old}}(336, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 2}\)