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

• Label: 1008.1.dc
• Level: $1008$
• Weight: $1$
• Character orbit: 1008.dc
• Rep. character: $\chi_{1008}(305,\cdot)$
• 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.dc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
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	76	4	72
Cusp forms	28	4	24
Eisenstein series	48	0	48

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

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

Trace form

\( 4 q - 2 q^{7} - 4 q^{13} - 2 q^{19} + 2 q^{25} - 2 q^{31} - 2 q^{37} + 4 q^{43} - 2 q^{49} + 8 q^{55} - 2 q^{67} - 2 q^{73} + 2 q^{79} + 2 q^{91}+O(q^{100}) \)

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.dc.a	$1008$	$1$	1008.dc	21.h	$6$	$4$	$2$	$0.503$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None			✓	✓	504.1.cu.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q+\beta _{1}q^{5}+(-1+\beta _{2})q^{7}+(\beta _{1}-\beta _{3})q^{11}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)