Space of modular forms of level 760, weight 2, and Character 760.cj

• Label: 760.2.cj
• Level: $760$
• Weight: $2$
• Character orbit: 760.cj
• Rep. character: $\chi_{760}(149,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $696$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 760 = 2^{3} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	760.cj (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 760 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(760, [\chi])\).

	Total	New	Old
Modular forms	744	744	0
Cusp forms	696	696	0
Eisenstein series	48	48	0

Trace form

696 * q - 6 * q^4 - 18 * q^6 - 24 * q^9 - 15 * q^10 - 42 * q^14 - 12 * q^15 - 6 * q^16 - 42 * q^20 - 36 * q^24 - 12 * q^25 + 18 * q^26 + 18 * q^30 - 84 * q^31 + 12 * q^34 + 30 * q^36 - 48 * q^39 - 18 * q^40 - 24 * q^41 - 36 * q^44 - 6 * q^46 + 264 * q^49 + 6 * q^50 - 60 * q^54 - 42 * q^55 - 108 * q^56 - 30 * q^60 - 30 * q^64 - 6 * q^65 - 48 * q^66 - 63 * q^70 - 24 * q^71 - 126 * q^74 - 48 * q^76 - 24 * q^79 + 45 * q^80 + 12 * q^81 - 126 * q^84 - 6 * q^86 - 24 * q^89 - 66 * q^90 + 36 * q^94 + 48 * q^95 - 72 * q^96

Decomposition of \(S_{2}^{\mathrm{new}}(760, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
760.2.cj.a	$760$	$2$	760.cj	760.bj	$18$	$696$	$116$	$6.069$		None		✓	✓	✓	760.2.cj.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{18}]$