Space of modular forms of level 315, weight 3, and Character 315.bd

• Label: 315.3.bd
• Level: $315$
• Weight: $3$
• Character orbit: 315.bd
• Rep. character: $\chi_{315}(191,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $128$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	315.bd (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(315, [\chi])\).

	Total	New	Old
Modular forms	200	128	72
Cusp forms	184	128	56
Eisenstein series	16	0	16

Trace form

\( 128 q + 128 q^{4} + 8 q^{6} + 2 q^{7} + 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(315, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.3.bd.a	$315$	$3$	315.bd	63.n	$6$	$128$	$64$	$8.583$		None		✓	✓	✓	315.3.s.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(2\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{3}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(315, [\chi]) \simeq \) \(S_{3}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 2}\)