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

• Label: 585.2.j
• Level: $585$
• Weight: $2$
• Character orbit: 585.j
• Rep. character: $\chi_{585}(406,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $48$
• Newform subspaces: $9$
• Sturm bound: $168$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.j (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 9 \)
Sturm bound:			\(168\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	184	48	136
Cusp forms	152	48	104
Eisenstein series	32	0	32

Trace form

\( 48 q - 26 q^{4} - 6 q^{7} + 12 q^{8} + O(q^{10}) \)

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.j.a	$585$	$2$	585.j	13.c	$3$	$2$	$1$	$4.671$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+2\zeta_{6}q^{4}+q^{5}+\zeta_{6}q^{7}+(6-6\zeta_{6})q^{11}+\cdots\)
585.2.j.b	$585$	$2$	585.j	13.c	$3$	$2$	$1$	$4.671$	\(\Q(\sqrt{-3}) \)	None		$2$	$0$	\(2\)	\(0\)	\(2\)	\(-5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(2-2\zeta_{6})q^{2}-2\zeta_{6}q^{4}+q^{5}-5\zeta_{6}q^{7}+\cdots\)
585.2.j.c	$585$	$2$	585.j	13.c	$3$	$4$	$2$	$4.671$	\(\Q(\zeta_{12})\)	None		$2$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\zeta_{12}+\zeta_{12}^{2})q^{2}+(-2+2\zeta_{12}+\cdots)q^{4}+\cdots\)
585.2.j.d	$585$	$2$	585.j	13.c	$3$	$4$	$2$	$4.671$	\(\Q(\sqrt{-3}, \sqrt{13})\)	None		$2$	$0$	\(-1\)	\(0\)	\(4\)	\(2\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{1}q^{2}+(-1+\beta _{1}+\beta _{2}+\beta _{3})q^{4}+\cdots\)
585.2.j.e	$585$	$2$	585.j	13.c	$3$	$4$	$2$	$4.671$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None		$2$	$0$	\(1\)	\(0\)	\(-4\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}-q^{5}+\cdots\)
585.2.j.f	$585$	$2$	585.j	13.c	$3$	$6$	$3$	$4.671$	6.0.1714608.1	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(-3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(-2\beta _{1}-\beta _{2}+\beta _{4}+\cdots)q^{4}+\cdots\)
585.2.j.g	$585$	$2$	585.j	13.c	$3$	$6$	$3$	$4.671$	6.0.591408.1	None		$2$	$0$	\(0\)	\(0\)	\(6\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{3}-\beta _{4}+\beta _{5})q^{4}+\cdots\)
585.2.j.h	$585$	$2$	585.j	13.c	$3$	$10$	$5$	$4.671$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(-2\)	\(0\)	\(10\)	\(-1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-1+\beta _{4}-\beta _{8})q^{4}+\cdots\)
585.2.j.i	$585$	$2$	585.j	13.c	$3$	$10$	$5$	$4.671$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(2\)	\(0\)	\(-10\)	\(-1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{3})q^{2}+(-1+\beta _{4}-\beta _{8}+\cdots)q^{4}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(585, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(39, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(117, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(195, [\chi])\)\(^{\oplus 2}\)