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

• Label: 1008.1.u
• Level: $1008$
• Weight: $1$
• Character orbit: 1008.u
• Rep. character: $\chi_{1008}(181,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $3$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1008.u (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 112 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	28	10	18
Cusp forms	12	6	6
Eisenstein series	16	4	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q + 2 q^{4} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.1.u.a	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}+iq^{7}-q^{8}+(1-i)q^{11}+\cdots\)
1008.1.u.b	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+iq^{2}-q^{4}-iq^{7}-iq^{8}+(1-i+\cdots)q^{11}+\cdots\)
1008.1.u.c	$1008$	$1$	1008.u	112.l	$4$	$2$	$1$	$0.503$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-7}) \)	None		$4$	$0$	\(2\)	\(0\)	\(0\)	\(0\)	$1$		\(q+q^{2}+q^{4}+iq^{7}+q^{8}+(-1+i+\cdots)q^{11}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)