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

• Label: 336.2.bj
• Level: $336$
• Weight: $2$
• Character orbit: 336.bj
• Rep. character: $\chi_{336}(95,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $7$
• Sturm bound: $128$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
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:			\(128\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(13\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	152	32	120
Cusp forms	104	32	72
Eisenstein series	48	0	48

Trace form

\( 32 q + O(q^{10}) \)

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.bj.a	$336$	$2$	336.bj	84.n	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$1$	\(0\)	\(-3\)	\(0\)	\(-5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2+\zeta_{6})q^{3}+(-3+\zeta_{6})q^{7}+(3+\cdots)q^{9}+\cdots\)
336.2.bj.b	$336$	$2$	336.bj	84.n	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(-2+\zeta_{6})q^{3}+(1-3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.c	$336$	$2$	336.bj	84.n	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(1\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2-\zeta_{6})q^{3}+(-1+3\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.d	$336$	$2$	336.bj	84.n	$6$	$2$	$1$	$2.683$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(3\)	\(0\)	\(5\)	$1$	$\mathrm{U}(1)[D_{6}]$	\(q+(2-\zeta_{6})q^{3}+(3-\zeta_{6})q^{7}+(3-3\zeta_{6})q^{9}+\cdots\)
336.2.bj.e	$336$	$2$	336.bj	84.n	$6$	$8$	$4$	$2.683$	8.0.8275904784.2	None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-\beta _{1}-\beta _{5}+\beta _{6})q^{3}+(1-\beta _{2}-\beta _{3}+\cdots)q^{5}+\cdots\)
336.2.bj.f	$336$	$2$	336.bj	84.n	$6$	$8$	$4$	$2.683$	8.0.303595776.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(1-2\beta _{2}+\beta _{4}+2\beta _{6})q^{5}+\cdots\)
336.2.bj.g	$336$	$2$	336.bj	84.n	$6$	$8$	$4$	$2.683$	8.0.8275904784.2	None		$4$	$0$	\(0\)	\(3\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{3}+(-\beta _{1}-\beta _{4}-\beta _{7})q^{5}+(3+\cdots)q^{7}+\cdots\)

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

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