Space of modular forms of level 860, weight 2, and Character 860.bj

• Label: 860.2.bj
• Level: $860$
• Weight: $2$
• Character orbit: 860.bj
• Rep. character: $\chi_{860}(47,\cdot)$
• Character field: $\Q(\zeta_{28})$
• Dimension: $1536$
• Newform subspaces: $1$
• Sturm bound: $264$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 860 = 2^{2} \cdot 5 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	860.bj (of order \(28\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 860 \)
Character field:			\(\Q(\zeta_{28})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(264\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(860, [\chi])\).

	Total	New	Old
Modular forms	1632	1632	0
Cusp forms	1536	1536	0
Eisenstein series	96	96	0

Trace form

1536 * q - 10 * q^2 - 20 * q^5 - 48 * q^6 - 10 * q^8 - 26 * q^10 - 14 * q^12 - 20 * q^13 - 60 * q^16 - 20 * q^17 + 40 * q^18 - 26 * q^20 - 56 * q^21 - 34 * q^22 - 20 * q^25 - 4 * q^26 - 50 * q^28 + 56 * q^30 + 90 * q^32 - 44 * q^33 - 80 * q^36 - 48 * q^37 - 2 * q^38 + 14 * q^40 - 40 * q^41 + 140 * q^42 - 60 * q^45 - 68 * q^46 - 46 * q^48 - 20 * q^50 - 6 * q^52 - 20 * q^53 - 56 * q^56 + 4 * q^57 - 46 * q^58 + 66 * q^60 - 40 * q^61 - 54 * q^62 - 20 * q^65 + 128 * q^66 + 54 * q^68 - 94 * q^70 - 130 * q^72 - 20 * q^73 + 44 * q^76 + 168 * q^77 - 126 * q^78 - 48 * q^81 - 126 * q^82 - 140 * q^86 - 106 * q^88 + 14 * q^90 - 212 * q^92 - 72 * q^93 - 120 * q^96 - 20 * q^97 - 60 * q^98

Decomposition of \(S_{2}^{\mathrm{new}}(860, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
860.2.bj.a	$860$	$2$	860.bj	860.aj	$28$	$1536$	$128$	$6.867$		None		✓	✓	✓	860.2.bj.a	$8$	$0$	\(-10\)	\(0\)	\(-20\)	\(0\)		$\mathrm{SU}(2)[C_{28}]$