Space of modular forms of level 583, weight 1, and Character 583.d

• Label: 583.1.d
• Level: $583$
• Weight: $1$
• Character orbit: 583.d
• Rep. character: $\chi_{583}(582,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $54$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 583 = 11 \cdot 53 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	583.d (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 583 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(54\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(583, [\chi])\).

	Total	New	Old
Modular forms	5	5	0
Cusp forms	3	3	0
Eisenstein series	2	2	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	3	0	0	0

Trace form

\( 3 q + q^{4} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(583, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
583.1.d.a	$583$	$1$	583.d	583.d	$2$	$1$	$1$	$0.291$	\(\Q\)	$D_{2}$	\(\Q(\sqrt{-11}) \), \(\Q(\sqrt{-583}) \)	\(\Q(\sqrt{53}) \)	✓	✓	583.1.d.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{4}+q^{9}+q^{11}+q^{16}+q^{25}-q^{36}+\cdots\)
583.1.d.b	$583$	$1$	583.d	583.d	$2$	$2$	$2$	$0.291$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-583}) \)	None	✓	✓	583.1.d.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{2}+q^{4}+q^{9}-q^{11}-q^{16}-\beta q^{18}+\cdots\)