Space of modular forms of level 315, weight 8, and Character 315.b

• Label: 315.8.b
• Level: $315$
• Weight: $8$
• Character orbit: 315.b
• Rep. character: $\chi_{315}(251,\cdot)$
• Character field: $\Q$
• Dimension: $72$
• Newform subspaces: $2$
• Sturm bound: $384$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	315.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(384\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(315, [\chi])\).

	Total	New	Old
Modular forms	344	72	272
Cusp forms	328	72	256
Eisenstein series	16	0	16

Trace form

72 * q - 4096 * q^4 - 1784 * q^7 + 175496 * q^16 + 447560 * q^22 + 1125000 * q^25 + 769720 * q^28 - 4092688 * q^37 + 3504848 * q^43 + 2072168 * q^46 + 96840 * q^49 - 3271096 * q^58 - 10305920 * q^64 - 12232224 * q^67 + 4533000 * q^70 - 811680 * q^79 - 77400344 * q^88 - 24467472 * q^91

Decomposition of \(S_{8}^{\mathrm{new}}(315, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.8.b.a	$315$	$8$	315.b	21.c	$2$	$36$	$36$	$98.401$		None		✓			315.8.b.a	$2$	$0$	\(0\)	\(0\)	\(-4500\)	\(-892\)		$\mathrm{SU}(2)[C_{2}]$
315.8.b.b	$315$	$8$	315.b	21.c	$2$	$36$	$36$	$98.401$		None		✓			315.8.b.a	$2$	$0$	\(0\)	\(0\)	\(4500\)	\(-892\)		$\mathrm{SU}(2)[C_{2}]$

Decomposition of \(S_{8}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{8}^{\mathrm{new}}(105, [\chi])\)\(^{\oplus 2}\)