Space of modular forms of level 580, weight 2, and Character 580.f

• Label: 580.2.f
• Level: $580$
• Weight: $2$
• Character orbit: 580.f
• Rep. character: $\chi_{580}(289,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• Newform subspaces: $1$
• Sturm bound: $180$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(180\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(580, [\chi])\).

	Total	New	Old
Modular forms	96	16	80
Cusp forms	84	16	68
Eisenstein series	12	0	12

Trace form

\( 16 q - 2 q^{5} + 28 q^{9} + 10 q^{25} - 8 q^{29} + 12 q^{35} - 20 q^{45} + 24 q^{51} - 24 q^{59} - 6 q^{65} + 72 q^{81} + 8 q^{91}+O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(580, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
580.2.f.a	$580$	$2$	580.f	145.d	$2$	$16$	$16$	$4.631$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		✓	✓	✓	580.2.f.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$2^{15}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+\beta _{9}q^{5}+\beta _{10}q^{7}+(2+\beta _{5}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(580, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(580, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 2}\)