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

• Label: 1008.2.k
• Level: $1008$
• Weight: $2$
• Character orbit: 1008.k
• Rep. character: $\chi_{1008}(881,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $3$
• Sturm bound: $384$
• Trace bound: $7$

Defining parameters

Level:	$N$	$=$	$1008 = 2^{4} \cdot 3^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1008.k (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$21$
Character field:			$\Q$
Newform subspaces:			$3$
Sturm bound:			$384$
Trace bound:			$7$
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	16	200
Cusp forms	168	16	152
Eisenstein series	48	0	48

Trace form

$16 q - 4 q^{7} + 32 q^{25} - 8 q^{43} + 16 q^{67} + 48 q^{79} - 16 q^{85} + 48 q^{91}+O(q^{100})$

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.k.a	$1008$	$2$	1008.k	21.c	$2$	$4$	$4$	$8.049$	$\Q(\sqrt{-2}, \sqrt{7})$	$\Q(\sqrt{-7})$					63.2.c.a	$4$	$0$	$0$	$0$	$0$	$0$	$2\cdot 3$	$\mathrm{U}(1)[D_{2}]$	$q-\beta _{2}q^{7}+(\beta _{1}-\beta _{3})q^{11}+(\beta _{1}+\beta _{3})q^{23}+\cdots$
1008.2.k.b	$1008$	$2$	1008.k	21.c	$2$	$4$	$4$	$8.049$	$\Q(\sqrt{-2}, \sqrt{3})$	None					252.2.f.a	$4$	$0$	$0$	$0$	$0$	$4$	$2^{2}\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta _{3}q^{5}+(1+\beta _{1})q^{7}-\beta _{2}q^{11}-2\beta _{1}q^{13}+\cdots$
1008.2.k.c	$1008$	$2$	1008.k	21.c	$2$	$8$	$8$	$8.049$	$\Q(\zeta_{16})$	None			✓		504.2.k.a	$4$	$0$	$0$	$0$	$0$	$-8$	$2^{9}$	$\mathrm{SU}(2)[C_{2}]$	$q-\beta_{7} q^{5}+(-\beta_{6}-1)q^{7}+(\beta_{2}+\beta_1)q^{11}+\cdots$

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

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