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

• Label: 315.2.k
• Level: $315$
• Weight: $2$
• Character orbit: 315.k
• Rep. character: $\chi_{315}(16,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $3$
• Sturm bound: $96$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.k (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
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	104	64	40
Cusp forms	88	64	24
Eisenstein series	16	0	16

Trace form

\( 64 q - 32 q^{4} + 8 q^{5} - 4 q^{6} - 2 q^{7} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
315.2.k.a	$315$	$2$	315.k	63.g	$3$	$4$	$2$	$2.515$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(1\)	\(0\)	\(-4\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(1+2\beta _{2})q^{3}+(-1+\beta _{1}+\cdots)q^{4}+\cdots\)
315.2.k.b	$315$	$2$	315.k	63.g	$3$	$24$	$12$	$2.515$		None		$2$	$0$	\(-1\)	\(1\)	\(-24\)	\(7\)		$\mathrm{SU}(2)[C_{3}]$
315.2.k.c	$315$	$2$	315.k	63.g	$3$	$36$	$18$	$2.515$		None		$2$	$0$	\(0\)	\(-1\)	\(36\)	\(-1\)		$\mathrm{SU}(2)[C_{3}]$

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

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