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

• Label: 1008.3.m
• Level: $1008$
• Weight: $3$
• Character orbit: 1008.m
• Rep. character: $\chi_{1008}(127,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $7$
• Sturm bound: $576$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1008.m (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(576\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	408	30	378
Cusp forms	360	30	330
Eisenstein series	48	0	48

Trace form

\( 30 q + 12 q^{5} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.3.m.a	$1008$	$3$	1008.m	4.b	$2$	$2$	$2$	$27.466$	\(\Q(\sqrt{-7}) \)	None		$2$	$0$	\(0\)	\(0\)	\(-16\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-8q^{5}-\beta q^{7}-4\beta q^{11}-4q^{13}+2q^{17}+\cdots\)
1008.3.m.b	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-1+\beta _{1})q^{5}-\beta _{3}q^{7}+(-\beta _{2}+\beta _{3})q^{11}+\cdots\)
1008.3.m.c	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	\(\Q(i, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 7$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+\beta _{2}q^{7}+\beta _{3}q^{11}+2q^{13}+\cdots\)
1008.3.m.d	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(1+\beta _{1})q^{5}-\beta _{3}q^{7}+(-2\beta _{2}+2\beta _{3})q^{11}+\cdots\)
1008.3.m.e	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(8\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{5}-\beta _{1}q^{7}+(4\beta _{1}+\beta _{3})q^{11}+(2+\cdots)q^{13}+\cdots\)
1008.3.m.f	$1008$	$3$	1008.m	4.b	$2$	$4$	$4$	$27.466$	\(\Q(\sqrt{-3}, \sqrt{-7})\)	None		$2$	$0$	\(0\)	\(0\)	\(20\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(5-\beta _{1})q^{5}+\beta _{3}q^{7}+(3\beta _{2}+5\beta _{3})q^{11}+\cdots\)
1008.3.m.g	$1008$	$3$	1008.m	4.b	$2$	$8$	$8$	$27.466$	8.0.49787136.1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{24}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}-\beta _{1}q^{7}-\beta _{2}q^{11}-10q^{13}+\cdots\)

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

\( S_{3}^{\mathrm{old}}(1008, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(12, [\chi])\)\(^{\oplus 12}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(24, [\chi])\)\(^{\oplus 8}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(36, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(48, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(56, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(72, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(144, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(168, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(504, [\chi])\)\(^{\oplus 2}\)