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

• Label: 1008.2.h
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.h
• Rep. character: $\chi_{1008}(575,\cdot)$
• Character field: $\Q$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.h (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	216	12	204
Cusp forms	168	12	156
Eisenstein series	48	0	48

Trace form

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

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1008.2.h.a	$1008$	$2$	1008.h	12.b	$2$	$4$	$4$	$8.049$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\zeta_{8}^{2}q^{5}+\zeta_{8}q^{7}+4\zeta_{8}^{3}q^{11}-4q^{13}+\cdots\)
1008.2.h.b	$1008$	$2$	1008.h	12.b	$2$	$8$	$8$	$8.049$	\(\Q(\zeta_{24})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q+(-\zeta_{24}^{2}+\zeta_{24}^{7})q^{5}-\zeta_{24}q^{7}+(-\zeta_{24}^{3}+\cdots)q^{11}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(1008, [\chi]) \cong \)