Space of modular forms of level 1008, weight 2, and Character 1008.cq

• Label: 1008.2.cq
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.cq
• Rep. character: $\chi_{1008}(431,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.cq (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 84 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(384\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1008, [\chi])\).

	Total	New	Old
Modular forms	432	32	400
Cusp forms	336	32	304
Eisenstein series	96	0	96

Trace form

\( 32 q - 16 q^{13} - 8 q^{25} - 8 q^{37} - 16 q^{49} + 16 q^{61} - 40 q^{73} + 96 q^{85} + 80 q^{97}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1008, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.2.cq.a	$1008$	$2$	1008.cq	84.n	$6$	$8$	$4$	$8.049$	8.0.796594176.1	None		✓			1008.2.cq.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{3}q^{5}-\beta _{6}q^{7}+(-\beta _{1}-\beta _{4})q^{11}+\cdots\)
1008.2.cq.b	$1008$	$2$	1008.cq	84.n	$6$	$12$	$6$	$8.049$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1008.2.cq.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{5}+\beta _{5}q^{7}+(-\beta _{1}+\beta _{8})q^{11}+\cdots\)
1008.2.cq.c	$1008$	$2$	1008.cq	84.n	$6$	$12$	$6$	$8.049$	\(\mathbb{Q}[x]/(x^{12} + \cdots)\)	None		✓			1008.2.cq.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{5}-\beta _{5}q^{7}+(\beta _{1}-\beta _{8})q^{11}+(-1+\cdots)q^{13}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)