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

• Label: 580.2.z
• Level: $580$
• Weight: $2$
• Character orbit: 580.z
• Rep. character: $\chi_{580}(121,\cdot)$
• Character field: $\Q(\zeta_{14})$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $180$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.z (of order \(14\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 29 \)
Character field:			\(\Q(\zeta_{14})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(180\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	576	60	516
Cusp forms	504	60	444
Eisenstein series	72	0	72

Trace form

60 * q + 2 * q^5 + 2 * q^9 + 4 * q^13 + 28 * q^21 - 12 * q^23 - 10 * q^25 + 42 * q^27 + 12 * q^29 + 14 * q^31 + 8 * q^35 + 14 * q^37 + 14 * q^39 - 10 * q^45 - 56 * q^47 - 24 * q^49 - 28 * q^51 - 4 * q^53 + 28 * q^55 - 104 * q^57 - 52 * q^59 - 56 * q^61 + 108 * q^63 - 18 * q^65 - 68 * q^67 - 78 * q^71 + 28 * q^73 + 98 * q^77 + 28 * q^79 - 36 * q^81 + 64 * q^83 + 54 * q^87 + 140 * q^89 - 82 * q^91 + 80 * q^93 + 28 * q^97

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.z.a	$580$	$2$	580.z	29.e	$14$	$24$	$4$	$4.631$		None		✓			580.2.z.a	$2$	$0$	\(0\)	\(0\)	\(-4\)	\(4\)		$\mathrm{SU}(2)[C_{14}]$
580.2.z.b	$580$	$2$	580.z	29.e	$14$	$36$	$6$	$4.631$		None		✓	✓		580.2.z.b	$2$	$0$	\(0\)	\(0\)	\(6\)	\(-4\)		$\mathrm{SU}(2)[C_{14}]$

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

\( S_{2}^{\mathrm{old}}(580, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(29, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(58, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(116, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(145, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(290, [\chi])\)\(^{\oplus 2}\)