Space of modular forms of level 1008, weight 1, and Character 1008.dd

• Label: 1008.1.dd
• Level: $1008$
• Weight: $1$
• Character orbit: 1008.dd
• Rep. character: $\chi_{1008}(79,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1008.dd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 252 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1008, [\chi])\).

	Total	New	Old
Modular forms	28	4	24
Cusp forms	4	4	0
Eisenstein series	24	0	24

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	4	0	0

Trace form

4 * q - 4 * q^5 + 2 * q^9 + 2 * q^13 - 2 * q^17 - 4 * q^21 + 2 * q^29 - 2 * q^33 + 2 * q^37 - 2 * q^41 - 2 * q^45 + 2 * q^49 + 2 * q^53 + 2 * q^57 - 2 * q^65 - 2 * q^69 - 2 * q^73 - 2 * q^77 - 2 * q^81 + 2 * q^85 - 2 * q^89 + 2 * q^97

Decomposition of \(S_{1}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.1.dd.a	$1008$	$1$	1008.dd	252.al	$6$	$4$	$2$	$0.503$	\(\Q(\zeta_{12})\)	$A_{4}$	None	None		✓	✓	✓	1008.1.bw.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+\zeta_{12}^{5}q^{3}-q^{5}+\zeta_{12}q^{7}-\zeta_{12}^{4}q^{9}+\cdots\)