Space of modular forms of level 1008, weight 3, and Character 1008.dc

• Label: 1008.3.dc
• Level: $1008$
• Weight: $3$
• Character orbit: 1008.dc
• Rep. character: $\chi_{1008}(305,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $7$
• Sturm bound: $576$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.dc (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(13\)
Distinguishing \(T_p\):			\(5\), \(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(1008, [\chi])\).

	Total	New	Old
Modular forms	816	64	752
Cusp forms	720	64	656
Eisenstein series	96	0	96

Trace form

\( 64 q + 16 q^{7} + 32 q^{19} + 144 q^{25} - 16 q^{31} - 64 q^{43} - 96 q^{49} - 96 q^{67} + 144 q^{73} - 48 q^{79} - 64 q^{85} + 416 q^{91} + 416 q^{97}+O(q^{100}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(1008, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.3.dc.a	$1008$	$3$	1008.dc	21.h	$6$	$4$	$2$	$27.466$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					126.3.s.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-26\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{5}+(-5-3\beta _{2})q^{7}+(5\beta _{1}-5\beta _{3})q^{11}+\cdots\)
1008.3.dc.b	$1008$	$3$	1008.dc	21.h	$6$	$4$	$2$	$27.466$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					126.3.s.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(14\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{5}+(7-7\beta _{2})q^{7}+(-3\beta _{1}+3\beta _{3})q^{11}+\cdots\)
1008.3.dc.c	$1008$	$3$	1008.dc	21.h	$6$	$4$	$2$	$27.466$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	None					252.3.bk.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(14\)	$3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{5}+(7-7\beta _{2})q^{7}+(5\beta _{1}-5\beta _{3})q^{11}+\cdots\)
1008.3.dc.d	$1008$	$3$	1008.dc	21.h	$6$	$8$	$4$	$27.466$	8.0.\(\cdots\).1	None					252.3.bk.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-12\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{5})q^{5}+(-2-\beta _{2}-\beta _{7})q^{7}+\cdots\)
1008.3.dc.e	$1008$	$3$	1008.dc	21.h	$6$	$12$	$6$	$27.466$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None					63.3.q.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$2^{4}\cdot 3^{5}$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{11}q^{5}+(2-\beta _{2}-\beta _{3}+4\beta _{8})q^{7}+\cdots\)
1008.3.dc.f	$1008$	$3$	1008.dc	21.h	$6$	$16$	$8$	$27.466$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					504.3.cu.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{12}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{6}q^{5}+(1+\beta _{4}+\beta _{9}+\beta _{11})q^{7}+\cdots\)
1008.3.dc.g	$1008$	$3$	1008.dc	21.h	$6$	$16$	$8$	$27.466$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None					504.3.cu.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(24\)	$2^{10}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{6}]$	\(q+(\beta _{4}+\beta _{6})q^{5}+(2-\beta _{1}-\beta _{3}-\beta _{15})q^{7}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(1008, [\chi])\) into lower level spaces

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