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

• Label: 1008.4.b
• Level: $1008$
• Weight: $4$
• Character orbit: 1008.b
• Rep. character: $\chi_{1008}(559,\cdot)$
• Character field: $\Q$
• Dimension: $60$
• Newform subspaces: $12$
• Sturm bound: $768$
• Trace bound: $25$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	1008.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 28 \)
Character field:			\(\Q\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(768\)
Trace bound:			\(25\)
Distinguishing \(T_p\):			\(5\), \(19\)

Dimensions

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

	Total	New	Old
Modular forms	600	60	540
Cusp forms	552	60	492
Eisenstein series	48	0	48

Trace form

\( 60 q + O(q^{10}) \)

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.b.a	$1008$	$4$	1008.b	28.d	$2$	$2$	$2$	$59.474$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-34\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+(-17+3\beta )q^{7}+23\beta q^{11}+\cdots\)
1008.4.b.b	$1008$	$4$	1008.b	28.d	$2$	$2$	$2$	$59.474$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-28\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-8\zeta_{6}q^{5}+(-14-7\zeta_{6})q^{7}-2\zeta_{6}q^{11}+\cdots\)
1008.4.b.c	$1008$	$4$	1008.b	28.d	$2$	$2$	$2$	$59.474$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-20\)	$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(-10-\zeta_{6})q^{7}+4\zeta_{6}q^{13}-56q^{19}+\cdots\)
1008.4.b.d	$1008$	$4$	1008.b	28.d	$2$	$2$	$2$	$59.474$	\(\Q(\sqrt{-3}) \)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(20\)	$2\cdot 3^{2}$	$\mathrm{U}(1)[D_{2}]$	\(q+(10-\zeta_{6})q^{7}-4\zeta_{6}q^{13}+56q^{19}+\cdots\)
1008.4.b.e	$1008$	$4$	1008.b	28.d	$2$	$2$	$2$	$59.474$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(28\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-8\zeta_{6}q^{5}+(14+7\zeta_{6})q^{7}+2\zeta_{6}q^{11}+\cdots\)
1008.4.b.f	$1008$	$4$	1008.b	28.d	$2$	$2$	$2$	$59.474$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(34\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{5}+(17-3\beta )q^{7}-23\beta q^{11}+30\beta q^{13}+\cdots\)
1008.4.b.g	$1008$	$4$	1008.b	28.d	$2$	$4$	$4$	$59.474$	\(\Q(\sqrt{-6}, \sqrt{7})\)	\(\Q(\sqrt{-21}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2\cdot 3^{4}$	$\mathrm{U}(1)[D_{2}]$	\(q-\beta _{1}q^{5}+7\beta _{3}q^{7}-\beta _{2}q^{11}-\beta _{1}q^{17}+\cdots\)
1008.4.b.h	$1008$	$4$	1008.b	28.d	$2$	$4$	$4$	$59.474$	\(\Q(\sqrt{-5}, \sqrt{7})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{5}+(-\beta _{1}+\beta _{2})q^{7}-2\beta _{2}q^{11}+\cdots\)
1008.4.b.i	$1008$	$4$	1008.b	28.d	$2$	$8$	$8$	$59.474$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4\)	$2^{15}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{5}+\beta _{3}q^{7}+(-\beta _{1}-\beta _{2}-\beta _{3}+\cdots)q^{11}+\cdots\)
1008.4.b.j	$1008$	$4$	1008.b	28.d	$2$	$8$	$8$	$59.474$	8.0.\(\cdots\).7	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{5}+(-\beta _{2}+\beta _{4}-\beta _{5})q^{7}+(-\beta _{2}+\cdots)q^{11}+\cdots\)
1008.4.b.k	$1008$	$4$	1008.b	28.d	$2$	$8$	$8$	$59.474$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(4\)	$2^{15}\cdot 3^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{5}q^{5}-\beta _{3}q^{7}+(\beta _{1}+\beta _{2}+\beta _{3}-\beta _{5}+\cdots)q^{11}+\cdots\)
1008.4.b.l	$1008$	$4$	1008.b	28.d	$2$	$16$	$16$	$59.474$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{40}\cdot 3^{6}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{4}q^{5}+\beta _{2}q^{7}-\beta _{6}q^{11}-\beta _{9}q^{13}+\cdots\)

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

\( S_{4}^{\mathrm{old}}(1008, [\chi]) \cong \)