Space of modular forms of level 315, weight 2, and Character 315.bb

• Label: 315.2.bb
• Level: $315$
• Weight: $2$
• Character orbit: 315.bb
• Rep. character: $\chi_{315}(89,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 105 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(315, [\chi])\).

	Total	New	Old
Modular forms	112	32	80
Cusp forms	80	32	48
Eisenstein series	32	0	32

Trace form

\( 32 q - 16 q^{4} - 12 q^{10} - 16 q^{16} - 24 q^{19} + 20 q^{25} - 24 q^{31} + 96 q^{40} - 24 q^{46} + 8 q^{49} - 24 q^{61} - 16 q^{64} - 48 q^{70} - 32 q^{79} - 128 q^{85} + 88 q^{91} + 48 q^{94}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(315, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.2.bb.a	$315$	$2$	315.bb	105.p	$6$	$8$	$4$	$2.515$	8.0.\(\cdots\).5	None		✓			315.2.bb.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+2\beta _{4}q^{4}+(\beta _{1}-\beta _{2}+\beta _{5})q^{5}+(\beta _{3}+\cdots)q^{7}+\cdots\)
315.2.bb.b	$315$	$2$	315.bb	105.p	$6$	$24$	$12$	$2.515$		None		✓	✓		315.2.bb.b	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$

Decomposition of \(S_{2}^{\mathrm{old}}(315, [\chi])\) into lower level spaces

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