Space of modular forms of level 1008, weight 2, and Character 1008.cj

• Label: 1008.2.cj
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.cj
• Rep. character: $\chi_{1008}(527,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $5$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cj (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 252 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

	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 \(S_{2}^{\mathrm{new}}(1008, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.2.cj.a	$1008$	$2$	1008.cj	252.ab	$6$	$2$	$1$	$8.049$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(0\)	\(-3\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(-1+\cdots)q^{7}+\cdots\)
1008.2.cj.b	$1008$	$2$	1008.cj	252.ab	$6$	$2$	$1$	$8.049$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1+2\zeta_{6})q^{3}+(-2+\zeta_{6})q^{5}+(1+\cdots)q^{7}+\cdots\)
1008.2.cj.c	$1008$	$2$	1008.cj	252.ab	$6$	$30$	$15$	$8.049$		None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-7\)		$\mathrm{SU}(2)[C_{6}]$
1008.2.cj.d	$1008$	$2$	1008.cj	252.ab	$6$	$30$	$15$	$8.049$		None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(7\)		$\mathrm{SU}(2)[C_{6}]$
1008.2.cj.e	$1008$	$2$	1008.cj	252.ab	$6$	$32$	$16$	$8.049$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)