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

• Label: 468.2.bd
• Level: $468$
• Weight: $2$
• Character orbit: 468.bd
• Rep. character: $\chi_{468}(191,\cdot)$
• 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.bd (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 - 3 * q^2 + q^4 - 12 * q^5 - 3 * q^6 - 2 * q^9 - 4 * q^10 - 7 * q^12 - 2 * q^13 - 6 * q^14 + q^16 + 4 * q^18 - 2 * q^21 + 9 * q^22 - 12 * q^24 + 60 * q^25 + 18 * q^26 + 6 * q^28 - 6 * q^29 - 21 * q^30 - 3 * q^32 + 10 * q^33 - 4 * q^34 + 7 * q^36 - 4 * q^37 - 42 * q^38 + 8 * q^40 - 4 * q^42 - 22 * q^45 - 6 * q^46 + 6 * q^48 - 116 * q^49 + 16 * q^52 + 22 * q^54 - 12 * q^57 + 11 * q^58 - 39 * q^60 - 4 * q^61 - 3 * q^62 - 26 * q^64 + 18 * q^65 + 30 * q^66 - 34 * q^69 - 27 * q^70 + 9 * q^72 - 16 * q^73 - 18 * q^76 + 12 * q^77 + 7 * q^78 - 90 * q^80 - 10 * q^81 + 11 * q^82 - 76 * q^84 - 8 * q^85 - 60 * q^86 - 3 * q^88 - 57 * q^90 - 36 * q^92 + 36 * q^93 + 66 * q^94 + 93 * q^96 - 4 * q^97 + 9 * q^98

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.bd.a	$468$	$2$	468.bd	468.ad	$6$	$160$	$80$	$3.737$		None		✓	✓	✓	468.2.bd.a	$4$	$0$	\(-3\)	\(0\)	\(-12\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$