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

• Label: 1008.2.ch
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.ch
• Rep. character: $\chi_{1008}(239,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $72$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.ch (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 36 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(384\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	408	72	336
Cusp forms	360	72	288
Eisenstein series	48	0	48

Trace form

\( 72 q - 12 q^{9} + O(q^{10}) \)

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.ch.a	$1008$	$2$	1008.ch	36.h	$6$	$24$	$12$	$8.049$		None		$2$	$0$	\(0\)	\(-6\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1008.2.ch.b	$1008$	$2$	1008.ch	36.h	$6$	$24$	$12$	$8.049$		None		$4$	$0$	\(0\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
1008.2.ch.c	$1008$	$2$	1008.ch	36.h	$6$	$24$	$12$	$8.049$		None		$2$	$0$	\(0\)	\(6\)	\(6\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)