Space of modular forms of level 468, weight 2, and Character 468.x

• Label: 468.2.x
• Level: $468$
• Weight: $2$
• Character orbit: 468.x
• Rep. character: $\chi_{468}(155,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $160$
• Newform subspaces: $1$
• Sturm bound: $168$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 468 = 2^{2} \cdot 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	468.x (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 468 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(168\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(468, [\chi])\).

	Total	New	Old
Modular forms	176	176	0
Cusp forms	160	160	0
Eisenstein series	16	16	0

Trace form

160 * q - 2 * q^4 - 8 * q^9 - 22 * q^12 - 2 * q^13 - 6 * q^14 - 2 * q^16 - 10 * q^22 - 68 * q^25 - 12 * q^29 - 18 * q^30 + 46 * q^36 + 12 * q^38 - 12 * q^40 + 28 * q^42 - 34 * q^48 - 60 * q^49 + 16 * q^52 + 36 * q^56 - 4 * q^61 + 28 * q^64 + 18 * q^65 - 86 * q^66 + 96 * q^68 + 36 * q^69 - 78 * q^74 - 60 * q^77 - 46 * q^78 + 24 * q^81 - 36 * q^82 + 26 * q^88 - 50 * q^90 - 36 * q^92 - 4 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(468, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
468.2.x.a	$468$	$2$	468.x	468.x	$6$	$160$	$80$	$3.737$		None		✓	✓	✓	468.2.x.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$