Space of modular forms of level 585, weight 1, and Character 585.o

• Label: 585.1.o
• Level: $585$
• Weight: $1$
• Character orbit: 585.o
• Rep. character: $\chi_{585}(298,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $84$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 585 = 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	585.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(84\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(585, [\chi])\).

	Total	New	Old
Modular forms	24	12	12
Cusp forms	8	8	0
Eisenstein series	16	4	12

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	8	0	0	0

Trace form

\( 8 q - 8 q^{10} - 8 q^{16} + 8 q^{22} + 8 q^{40} - 8 q^{43} - 8 q^{52} - 8 q^{82} + 16 q^{88}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(585, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
585.1.o.a	$585$	$1$	585.o	65.h	$4$	$8$	$4$	$0.292$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-39}) \)	None		✓	✓	✓	585.1.o.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{16}^{5}-\zeta_{16}^{7})q^{2}+(-\zeta_{16}^{2}+\zeta_{16}^{4}+\cdots)q^{4}+\cdots\)