Space of modular forms of level 585, weight 2, and Character 585.i

• Label: 585.2.i
• Level: $585$
• Weight: $2$
• Character orbit: 585.i
• Rep. character: $\chi_{585}(196,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $96$
• Newform subspaces: $8$
• Sturm bound: $168$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 8 \)
Sturm bound:			\(168\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(2\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(585, [\chi])\).

	Total	New	Old
Modular forms	176	96	80
Cusp forms	160	96	64
Eisenstein series	16	0	16

Trace form

\( 96 q + 4 q^{2} + 4 q^{3} - 48 q^{4} + 4 q^{5} - 4 q^{6} - 24 q^{8} + 16 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(585, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
585.2.i.a	$585$	$2$	585.i	9.c	$3$	$2$	$1$	$4.671$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(3\)	\(-1\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-\zeta_{6})q^{3}+2\zeta_{6}q^{4}-\zeta_{6}q^{5}+(4+\cdots)q^{7}+\cdots\)
585.2.i.b	$585$	$2$	585.i	9.c	$3$	$2$	$1$	$4.671$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(0\)	\(1\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(-1+2\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
585.2.i.c	$585$	$2$	585.i	9.c	$3$	$2$	$1$	$4.671$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(1\)	\(3\)	\(1\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(1-\zeta_{6})q^{2}+(2-\zeta_{6})q^{3}+\zeta_{6}q^{4}+\cdots\)
585.2.i.d	$585$	$2$	585.i	9.c	$3$	$2$	$1$	$4.671$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(-3\)	\(1\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}+(-2+\zeta_{6})q^{3}-2\zeta_{6}q^{4}+\cdots\)
585.2.i.e	$585$	$2$	585.i	9.c	$3$	$16$	$8$	$4.671$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(-3\)	\(1\)	\(8\)	\(11\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{6}q^{2}+(-\beta _{7}+\beta _{14})q^{3}+(-\beta _{1}+\cdots)q^{4}+\cdots\)
585.2.i.f	$585$	$2$	585.i	9.c	$3$	$16$	$8$	$4.671$	\(\mathbb{Q}[x]/(x^{16} - \cdots)\)	None		$2$	$0$	\(1\)	\(-2\)	\(-8\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(-\beta _{1}-\beta _{3}-\beta _{4}-\beta _{5}-\beta _{6}+\cdots)q^{3}+\cdots\)
585.2.i.g	$585$	$2$	585.i	9.c	$3$	$26$	$13$	$4.671$		None		$2$	$0$	\(1\)	\(1\)	\(-13\)	\(-10\)		$\mathrm{SU}(2)[C_{3}]$
585.2.i.h	$585$	$2$	585.i	9.c	$3$	$30$	$15$	$4.671$		None		$2$	$0$	\(1\)	\(1\)	\(15\)	\(-10\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(585, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)