Space of modular forms of level 315, weight 4, and Character 315.bb

• Label: 315.4.bb
• Level: $315$
• Weight: $4$
• Character orbit: 315.bb
• Rep. character: $\chi_{315}(89,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $96$
• Newform subspaces: $1$
• Sturm bound: $192$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	315.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(192\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(315, [\chi])\).

	Total	New	Old
Modular forms	304	96	208
Cusp forms	272	96	176
Eisenstein series	32	0	32

Trace form

96 * q - 192 * q^4 - 72 * q^10 - 768 * q^16 + 432 * q^19 - 324 * q^25 - 1656 * q^31 - 1476 * q^40 + 1704 * q^46 - 1608 * q^49 - 2592 * q^61 + 6864 * q^64 - 3660 * q^70 + 2184 * q^79 + 3168 * q^85 + 3672 * q^91 - 3240 * q^94

Decomposition of \(S_{4}^{\mathrm{new}}(315, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.4.bb.a	$315$	$4$	315.bb	105.p	$6$	$96$	$48$	$18.586$		None		✓	✓	✓	315.4.bb.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{4}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

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