Space of modular forms of level 579, weight 1, and Character 579.s

• Label: 579.1.s
• Level: $579$
• Weight: $1$
• Character orbit: 579.s
• Rep. character: $\chi_{579}(8,\cdot)$
• Character field: $\Q(\zeta_{32})$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 579 = 3 \cdot 193 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	579.s (of order \(32\) and degree \(16\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 579 \)
Character field:			\(\Q(\zeta_{32})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(579, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	16	16	0
Eisenstein series	32	32	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(579, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
579.1.s.a	$579$	$1$	579.s	579.s	$32$	$16$	$1$	$0.289$	\(\Q(\zeta_{32})\)	$D_{32}$	\(\Q(\sqrt{-3}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{32}^{10}q^{3}-\zeta_{32}^{2}q^{4}+(\zeta_{32}+\zeta_{32}^{7}+\cdots)q^{7}+\cdots\)