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

• Label: 580.2.x
• Level: $580$
• Weight: $2$
• Character orbit: 580.x
• Rep. character: $\chi_{580}(9,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $96$
• 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.x (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{14})\)
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	576	96	480
Cusp forms	504	96	408
Eisenstein series	72	0	72

Trace form

96 * q + 2 * q^5 - 28 * q^9 - 14 * q^15 - 28 * q^21 + 18 * q^25 + 22 * q^29 - 14 * q^31 + 30 * q^35 + 14 * q^39 - 15 * q^45 + 42 * q^49 - 24 * q^51 - 56 * q^55 - 60 * q^59 - 56 * q^61 - 29 * q^65 + 56 * q^69 + 42 * q^71 + 82 * q^81 - 70 * q^85 + 118 * q^91 - 112 * q^95

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.x.a	$580$	$2$	580.x	145.l	$14$	$96$	$16$	$4.631$		None		✓	✓	✓	580.2.x.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)		$\mathrm{SU}(2)[C_{14}]$

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

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