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

• Label: 1008.2.b
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.b
• Rep. character: $\chi_{1008}(559,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $9$
• Sturm bound: $384$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(384\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(5\), \(11\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	216	20	196
Cusp forms	168	20	148
Eisenstein series	48	0	48

Trace form

\( 20 q + 4 q^{25} - 24 q^{29} + 8 q^{37} + 20 q^{49} + 24 q^{53} + 24 q^{77} + 48 q^{85}+O(q^{100}) \)

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.b.a	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	\(\Q(\sqrt{-3}) \)	None					336.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta-2)q^{7}-2\beta q^{11}-4\beta q^{17}-4 q^{19}+\cdots\)
1008.2.b.b	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	\(\Q(\sqrt{-3}) \)	None					112.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{5}+(-\beta-2)q^{7}+2\beta q^{11}+\cdots\)
1008.2.b.c	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			1008.2.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(\beta-2)q^{7}-4\beta q^{13}+8 q^{19}+5 q^{25}+\cdots\)
1008.2.b.d	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	\(\Q(\sqrt{-6}) \)	None					336.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+(-1-\beta )q^{7}-\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.e	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	\(\Q(\sqrt{-6}) \)	None					336.2.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+(1+\beta )q^{7}+\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.f	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		✓			1008.2.b.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q+(-\beta+2)q^{7}-4\beta q^{13}-8 q^{19}+\cdots\)
1008.2.b.g	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	\(\Q(\sqrt{-3}) \)	None					112.2.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta q^{5}+(\beta+2)q^{7}-2\beta q^{11}-2\beta q^{13}+\cdots\)
1008.2.b.h	$1008$	$2$	1008.b	28.d	$2$	$2$	$2$	$8.049$	\(\Q(\sqrt{-3}) \)	None					336.2.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta+2)q^{7}-2\beta q^{11}+4\beta q^{17}+4 q^{19}+\cdots\)
1008.2.b.i	$1008$	$2$	1008.b	28.d	$2$	$4$	$4$	$8.049$	\(\Q(\sqrt{-6}, \sqrt{7})\)	\(\Q(\sqrt{-21}) \)		✓	✓		1008.2.b.i	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{5}-\beta _{3}q^{7}-\beta _{2}q^{11}+3\beta _{1}q^{17}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(28, [\chi])\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(84, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(112, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(252, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(336, [\chi])\)\(^{\oplus 2}\)