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

• Label: 1008.1.dt
• Level: $1008$
• Weight: $1$
• Character orbit: 1008.dt
• Rep. character: $\chi_{1008}(163,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $8$
• 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.dt (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(\zeta_{12})\)
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	40	16	24
Cusp forms	8	8	0
Eisenstein series	32	8	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	8	0

Trace form

\( 8 q - 4 q^{7} + 8 q^{13} + 4 q^{16} + 8 q^{22} - 4 q^{40} + 4 q^{46} - 4 q^{49} - 4 q^{52} - 8 q^{55} + 4 q^{58} - 4 q^{61} - 4 q^{82} - 4 q^{91} - 4 q^{94} + 8 q^{97}+O(q^{100}) \)

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.dt.a	$1008$	$1$	1008.dt	112.u	$12$	$8$	$2$	$0.503$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		✓	✓	✓	1008.1.dt.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$1$		\(q-\zeta_{24}^{11}q^{2}-\zeta_{24}^{10}q^{4}+\zeta_{24}^{11}q^{5}+\cdots\)