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

• Label: 315.2.bl
• Level: $315$
• Weight: $2$
• Character orbit: 315.bl
• Rep. character: $\chi_{315}(41,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $64$
• Newform subspaces: $10$
• Sturm bound: $96$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bl (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 10 \)
Sturm bound:			\(96\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(2\), \(11\), \(13\), \(17\)

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

\( 64 q + 32 q^{4} + 2 q^{7} + 8 q^{9} + O(q^{10}) \)

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.bl.a	$315$	$2$	315.bl	63.o	$6$	$2$	$1$	$2.515$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(-3\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
315.2.bl.b	$315$	$2$	315.bl	63.o	$6$	$2$	$1$	$2.515$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(0\)	\(-1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
315.2.bl.c	$315$	$2$	315.bl	63.o	$6$	$2$	$1$	$2.515$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(-3\)	\(0\)	\(1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
315.2.bl.d	$315$	$2$	315.bl	63.o	$6$	$2$	$1$	$2.515$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(-3\)	\(3\)	\(1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
315.2.bl.e	$315$	$2$	315.bl	63.o	$6$	$2$	$1$	$2.515$	\(\Q(\sqrt{-3}) \)	None		$2$	$1$	\(0\)	\(-3\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{3}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+\cdots\)
315.2.bl.f	$315$	$2$	315.bl	63.o	$6$	$2$	$1$	$2.515$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(-3\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+\cdots\)
315.2.bl.g	$315$	$2$	315.bl	63.o	$6$	$2$	$1$	$2.515$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(-1\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(2-\zeta_{6})q^{3}-2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(-3+\cdots)q^{7}+\cdots\)
315.2.bl.h	$315$	$2$	315.bl	63.o	$6$	$2$	$1$	$2.515$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\zeta_{6}q^{5}+(-1+\cdots)q^{7}+\cdots\)
315.2.bl.i	$315$	$2$	315.bl	63.o	$6$	$24$	$12$	$2.515$		None		$2$	$0$	\(6\)	\(-5\)	\(12\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$
315.2.bl.j	$315$	$2$	315.bl	63.o	$6$	$24$	$12$	$2.515$		None		$2$	$0$	\(6\)	\(5\)	\(-12\)	\(9\)		$\mathrm{SU}(2)[C_{6}]$

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

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