Space of modular forms of level 588, weight 8, and Character 588.f

• Label: 588.8.f
• Level: $588$
• Weight: $8$
• Character orbit: 588.f
• Rep. character: $\chi_{588}(293,\cdot)$
• Character field: $\Q$
• Dimension: $94$
• Newform subspaces: $3$
• Sturm bound: $896$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$588 = 2^{2} \cdot 3 \cdot 7^{2}$
Weight:	$k$	$=$	$8$
Character orbit:	$[\chi]$	$=$	588.f (of order $2$ and degree $1$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$21$
Character field:			$\Q$
Newform subspaces:			$3$
Sturm bound:			$896$
Trace bound:			$1$
Distinguishing $T_p$:			$5$

Dimensions

The following table gives the dimensions of various subspaces of $M_{8}(588, [\chi])$.

	Total	New	Old
Modular forms	808	94	714
Cusp forms	760	94	666
Eisenstein series	48	0	48

Trace form

94 * q - 2656 * q^9 + 16206 * q^15 + 1652774 * q^25 - 667970 * q^37 - 1262066 * q^39 - 260702 * q^43 - 234786 * q^51 - 1854628 * q^57 - 790362 * q^67 + 31760182 * q^79 + 3226512 * q^81 + 7216788 * q^85 + 7009824 * q^93 + 21405058 * q^99

Decomposition of $S_{8}^{\mathrm{new}}(588, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
588.8.f.a	$588$	$8$	588.f	21.c	$2$	$2$	$2$	$183.682$	$\Q(\sqrt{-3})$	$\Q(\sqrt{-3})$					84.8.k.a	$4$	$0$	$0$	$0$	$0$	$0$	$2$	$\mathrm{U}(1)[D_{2}]$	$q+27\beta q^{3}-2187 q^{9}+5541\beta q^{13}+\cdots$
588.8.f.b	$588$	$8$	588.f	21.c	$2$	$36$	$36$	$183.682$		None					84.8.k.b	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$
588.8.f.c	$588$	$8$	588.f	21.c	$2$	$56$	$56$	$183.682$		None		✓	✓		588.8.f.c	$4$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{2}]$

Decomposition of $S_{8}^{\mathrm{old}}(588, [\chi])$ into lower level spaces

$S_{8}^{\mathrm{old}}(588, [\chi]) \simeq$ $S_{8}^{\mathrm{new}}(21, [\chi])$$^{\oplus 6}$$\oplus$$S_{8}^{\mathrm{new}}(42, [\chi])$$^{\oplus 4}$$\oplus$$S_{8}^{\mathrm{new}}(84, [\chi])$$^{\oplus 2}$$\oplus$$S_{8}^{\mathrm{new}}(147, [\chi])$$^{\oplus 3}$$\oplus$$S_{8}^{\mathrm{new}}(294, [\chi])$$^{\oplus 2}$