Space of modular forms of level 1008, weight 4, and Character 1008.k

• Label: 1008.4.k
• Level: $1008$
• Weight: $4$
• Character orbit: 1008.k
• Rep. character: $\chi_{1008}(881,\cdot)$
• Character field: $\Q$
• Dimension: $48$
• Newform subspaces: $5$
• Sturm bound: $768$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1008.k (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 5 \)
Sturm bound:			\(768\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(1008, [\chi])\).

	Total	New	Old
Modular forms	600	48	552
Cusp forms	552	48	504
Eisenstein series	48	0	48

Trace form

\( 48 q - 36 q^{7} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(1008, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.4.k.a	$1008$	$4$	1008.k	21.c	$2$	$4$	$4$	$59.474$	\(\Q(\sqrt{-2}, \sqrt{7})\)	\(\Q(\sqrt{-7}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q-7\beta _{2}q^{7}+(-6\beta _{1}-7\beta _{3})q^{11}+(-2^{4}\beta _{1}+\cdots)q^{23}+\cdots\)
1008.4.k.b	$1008$	$4$	1008.k	21.c	$2$	$4$	$4$	$59.474$	\(\Q(\sqrt{-2}, \sqrt{111})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(44\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+(11+\beta _{2})q^{7}-11\beta _{1}q^{11}+\cdots\)
1008.4.k.c	$1008$	$4$	1008.k	21.c	$2$	$8$	$8$	$59.474$	8.0.\(\cdots\).6	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-40\)	$2^{9}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+(-5+\beta _{4}+\beta _{5})q^{7}+(5\beta _{1}+\cdots)q^{11}+\cdots\)
1008.4.k.d	$1008$	$4$	1008.k	21.c	$2$	$8$	$8$	$59.474$	8.0.\(\cdots\).9	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-16\)	$2^{10}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{3}q^{5}+(-2+\beta _{2})q^{7}+\beta _{5}q^{11}+\cdots\)
1008.4.k.e	$1008$	$4$	1008.k	21.c	$2$	$24$	$24$	$59.474$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{4}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 10}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(42, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)