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

• Label: 585.2.w
• Level: $585$
• Weight: $2$
• Character orbit: 585.w
• Rep. character: $\chi_{585}(73,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $66$
• Newform subspaces: $7$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.w (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 7 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
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	184	74	110
Cusp forms	152	66	86
Eisenstein series	32	8	24

Trace form

\( 66 q + 6 q^{2} + 62 q^{4} + 4 q^{5} + 18 q^{8} + O(q^{10}) \)

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.w.a	$585$	$2$	585.w	65.k	$4$	$2$	$1$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$1$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}-q^{4}+(-2-i)q^{5}-4iq^{7}+\cdots\)
585.2.w.b	$585$	$2$	585.w	65.k	$4$	$2$	$1$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(-2\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-q^{2}-q^{4}+(1+2i)q^{5}+2iq^{7}+3q^{8}+\cdots\)
585.2.w.c	$585$	$2$	585.w	65.k	$4$	$2$	$1$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+q^{2}-q^{4}+(2+i)q^{5}-4iq^{7}-3q^{8}+\cdots\)
585.2.w.d	$585$	$2$	585.w	65.k	$4$	$4$	$2$	$4.671$	\(\Q(\zeta_{8})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$5$	$\mathrm{SU}(2)[C_{4}]$	\(q-2q^{4}+\zeta_{8}^{2}q^{5}-3\zeta_{8}q^{7}+(-2\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
585.2.w.e	$585$	$2$	585.w	65.k	$4$	$8$	$4$	$4.671$	8.0.619810816.2	None		$2$	$0$	\(4\)	\(0\)	\(-2\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{5}q^{2}+(1+\beta _{4}-\beta _{5}-\beta _{7})q^{4}+(-\beta _{3}+\cdots)q^{5}+\cdots\)
585.2.w.f	$585$	$2$	585.w	65.k	$4$	$20$	$10$	$4.671$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{11}q^{2}+(2-\beta _{2})q^{4}+\beta _{8}q^{5}+\beta _{6}q^{7}+\cdots\)
585.2.w.g	$585$	$2$	585.w	65.k	$4$	$28$	$14$	$4.671$		None		$2$	$0$	\(4\)	\(0\)	\(4\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)