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

• Label: 585.2.b
• Level: $585$
• Weight: $2$
• Character orbit: 585.b
• Rep. character: $\chi_{585}(181,\cdot)$
• Character field: $\Q$
• Dimension: $22$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $14$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(168\)
Trace bound:			\(14\)
Distinguishing \(T_p\):			\(2\), \(7\), \(17\)

Dimensions

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

	Total	New	Old
Modular forms	92	22	70
Cusp forms	76	22	54
Eisenstein series	16	0	16

Trace form

\( 22 q - 18 q^{4} + O(q^{10}) \)

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.b.a	$585$	$2$	585.b	13.b	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+iq^{5}+2iq^{7}+3iq^{8}+\cdots\)
585.2.b.b	$585$	$2$	585.b	13.b	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+iq^{5}+4iq^{7}+3iq^{8}+\cdots\)
585.2.b.c	$585$	$2$	585.b	13.b	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+q^{4}+iq^{5}-4iq^{7}+3iq^{8}+\cdots\)
585.2.b.d	$585$	$2$	585.b	13.b	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+iq^{5}-3iq^{7}-3iq^{11}+(2+\cdots)q^{13}+\cdots\)
585.2.b.e	$585$	$2$	585.b	13.b	$2$	$4$	$4$	$4.671$	\(\Q(i, \sqrt{17})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-3+\beta _{3})q^{4}-\beta _{2}q^{5}+(-\beta _{1}+\cdots)q^{7}+\cdots\)
585.2.b.f	$585$	$2$	585.b	13.b	$2$	$4$	$4$	$4.671$	\(\Q(i, \sqrt{13})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-2\beta _{1}q^{2}-2q^{4}+\beta _{1}q^{5}-\beta _{2}q^{7}+\cdots\)
585.2.b.g	$585$	$2$	585.b	13.b	$2$	$6$	$6$	$4.671$	6.0.5089536.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{5}q^{2}+(-2+\beta _{3})q^{4}+\beta _{4}q^{5}+(-\beta _{2}+\cdots)q^{7}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)