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

• Label: 580.2.bc
• Level: $580$
• Weight: $2$
• Character orbit: 580.bc
• Rep. character: $\chi_{580}(37,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $180$
• 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.bc (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 145 \)
Character field:			\(\Q(\zeta_{28})\)
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	1152	180	972
Cusp forms	1008	180	828
Eisenstein series	144	0	144

Trace form

180 * q - 38 * q^9 + 4 * q^11 - 22 * q^13 - 6 * q^15 + 32 * q^21 + 30 * q^25 + 30 * q^27 + 32 * q^31 - 4 * q^33 - 40 * q^35 - 18 * q^37 + 12 * q^39 - 10 * q^41 + 44 * q^43 + 20 * q^45 + 32 * q^47 + 84 * q^49 - 52 * q^53 + 26 * q^55 - 24 * q^57 + 22 * q^61 - 136 * q^63 + 10 * q^65 - 16 * q^67 - 104 * q^69 - 28 * q^73 + 36 * q^75 + 42 * q^77 + 20 * q^79 - 70 * q^81 - 56 * q^83 + 56 * q^85 - 146 * q^87 + 6 * q^89 - 44 * q^93 + 188 * q^95 + 128 * q^97 + 56 * q^99

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.bc.a	$580$	$2$	580.bc	145.t	$28$	$180$	$15$	$4.631$		None		✓	✓	✓	580.2.bc.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$

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

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