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

• Label: 580.2.bh
• Level: $580$
• Weight: $2$
• Character orbit: 580.bh
• Rep. character: $\chi_{580}(63,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $1032$
• Newform subspaces: $3$
• Sturm bound: $180$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 580 = 2^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	580.bh (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 580 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(180\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(13\)

Dimensions

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

	Total	New	Old
Modular forms	1128	1128	0
Cusp forms	1032	1032	0
Eisenstein series	96	96	0

Trace form

1032 * q - 14 * q^2 - 20 * q^5 - 20 * q^6 - 14 * q^8 - 14 * q^10 - 16 * q^13 - 20 * q^16 + 84 * q^18 - 26 * q^20 - 56 * q^21 - 2 * q^22 - 40 * q^25 - 28 * q^26 - 40 * q^28 - 4 * q^30 - 14 * q^32 - 12 * q^33 - 52 * q^36 - 28 * q^37 - 60 * q^38 - 14 * q^40 - 54 * q^42 - 10 * q^45 - 126 * q^48 - 14 * q^50 - 116 * q^52 - 10 * q^53 - 196 * q^56 - 72 * q^57 - 150 * q^58 - 14 * q^60 - 56 * q^61 - 32 * q^62 + 30 * q^65 - 196 * q^66 - 168 * q^68 - 14 * q^72 + 154 * q^73 - 28 * q^76 - 28 * q^77 - 30 * q^78 - 124 * q^80 + 148 * q^81 + 30 * q^82 - 28 * q^85 - 56 * q^86 + 56 * q^88 - 14 * q^90 + 22 * q^92 + 4 * q^93 - 92 * q^96 - 98 * q^97 - 14 * q^98

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.bh.a	$580$	$2$	580.bh	580.ah	$28$	$12$	$1$	$4.631$	\(\Q(\zeta_{28})\)	\(\Q(\sqrt{-1}) \)		✓			580.2.bh.a	$4$	$0$	\(-2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{28}]$	\(q+(-\zeta_{28}^{2}-\zeta_{28}^{9})q^{2}+2\zeta_{28}^{11}q^{4}+\cdots\)
580.2.bh.b	$580$	$2$	580.bh	580.ah	$28$	$12$	$1$	$4.631$	\(\Q(\zeta_{28})\)	\(\Q(\sqrt{-1}) \)		✓			580.2.bh.a	$4$	$0$	\(2\)	\(0\)	\(-4\)	\(0\)	$1$	$\mathrm{U}(1)[D_{28}]$	\(q+(\zeta_{28}^{2}+\zeta_{28}^{9})q^{2}+2\zeta_{28}^{11}q^{4}+\cdots\)
580.2.bh.c	$580$	$2$	580.bh	580.ah	$28$	$1008$	$84$	$4.631$		None		✓	✓		580.2.bh.c	$8$	$0$	\(-14\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$