Space of modular forms of level 580, weight 1, and Character 580.y

• Label: 580.1.y
• Level: $580$
• Weight: $1$
• Character orbit: 580.y
• Rep. character: $\chi_{580}(179,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $24$
• Newform subspaces: $3$
• Sturm bound: $90$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	580.y (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 580 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(90\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(580, [\chi])\).

	Total	New	Old
Modular forms	48	48	0
Cusp forms	24	24	0
Eisenstein series	24	24	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q - 10 q^{6} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(580, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
580.1.y.a	$580$	$1$	580.y	580.y	$14$	$6$	$1$	$0.289$	\(\Q(\zeta_{14})\)	$D_{14}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-1\)	\(0\)	\(1\)	\(0\)	$1$		\(q-\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}-\zeta_{14}^{4}q^{5}-\zeta_{14}^{3}q^{8}+\cdots\)
580.1.y.b	$580$	$1$	580.y	580.y	$14$	$6$	$1$	$0.289$	\(\Q(\zeta_{14})\)	$D_{14}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(1\)	\(0\)	\(1\)	\(0\)	$1$		\(q+\zeta_{14}q^{2}+\zeta_{14}^{2}q^{4}+\zeta_{14}^{5}q^{5}+\zeta_{14}^{3}q^{8}+\cdots\)
580.1.y.c	$580$	$1$	580.y	580.y	$14$	$12$	$2$	$0.289$	\(\Q(\zeta_{28})\)	$D_{14}$	\(\Q(\sqrt{-5}) \)	None		$8$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+\zeta_{28}^{9}q^{2}+(\zeta_{28}+\zeta_{28}^{5})q^{3}-\zeta_{28}^{4}q^{4}+\cdots\)