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

• Label: 585.2.c
• Level: $585$
• Weight: $2$
• Character orbit: 585.c
• Rep. character: $\chi_{585}(469,\cdot)$
• Character field: $\Q$
• Dimension: $30$
• Newform subspaces: $4$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	92	30	62
Cusp forms	76	30	46
Eisenstein series	16	0	16

Trace form

\( 30 q - 26 q^{4} + 4 q^{5} + O(q^{10}) \)

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.c.a	$585$	$2$	585.c	5.b	$2$	$2$	$2$	$4.671$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2q^{4}+(1+2i)q^{5}-iq^{7}+q^{11}+\cdots\)
585.2.c.b	$585$	$2$	585.c	5.b	$2$	$6$	$6$	$4.671$	6.0.350464.1	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{2}]$	\(q+(\beta _{3}-\beta _{5})q^{2}+(-2-\beta _{1}-\beta _{2})q^{4}+\cdots\)
585.2.c.c	$585$	$2$	585.c	5.b	$2$	$10$	$10$	$4.671$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-1-\beta _{4}+\beta _{6}+\beta _{7})q^{4}+\cdots\)
585.2.c.d	$585$	$2$	585.c	5.b	$2$	$12$	$12$	$4.671$	12.0.\(\cdots\).1	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}+(-1-\beta _{9})q^{4}+(-\beta _{5}+\beta _{8}+\cdots)q^{5}+\cdots\)

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

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