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

• Label: 585.2.r
• Level: $585$
• Weight: $2$
• Character orbit: 585.r
• Rep. character: $\chi_{585}(161,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	585.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 39 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(7\)
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	32	152
Cusp forms	152	32	120
Eisenstein series	32	0	32

Trace form

\( 32 q + 16 q^{7} + 16 q^{16} + 16 q^{19} + 32 q^{34} - 48 q^{37} + 80 q^{46} - 80 q^{52} - 16 q^{55} + 96 q^{58} - 16 q^{61} + 64 q^{73} - 96 q^{76} + 16 q^{79} - 80 q^{91} - 32 q^{94} - 80 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
585.2.r.a	$585$	$2$	585.r	39.f	$4$	$8$	$4$	$4.671$	\(\Q(\zeta_{24})\)	None		✓			585.2.r.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta_{2} q^{2}+\beta_{3} q^{4}+\beta_1 q^{5}+(-\beta_{6}-\beta_{4}-\beta_{3}-1)q^{7}+\cdots\)
585.2.r.b	$585$	$2$	585.r	39.f	$4$	$8$	$4$	$4.671$	8.0.959512576.1	None		✓			585.2.r.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-2\beta _{2}q^{4}+\beta _{5}q^{5}+(1+\beta _{2}+\beta _{4})q^{7}+\cdots\)
585.2.r.c	$585$	$2$	585.r	39.f	$4$	$16$	$8$	$4.671$	16.0.\(\cdots\).7	None		✓	✓		585.2.r.c	$4$	$0$	\(0\)	\(0\)	\(0\)	\(16\)	$2^{8}$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-\beta _{4}-\beta _{6}-\beta _{10})q^{2}+(-\beta _{1}+\beta _{15})q^{4}+\cdots\)

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

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