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

• Label: 468.2.k
• Level: $468$
• Weight: $2$
• Character orbit: 468.k
• Rep. character: $\chi_{468}(61,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $28$
• 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.k (of order $3$ and degree $2$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$117$
Character field:			$\Q(\zeta_{3})$
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	180	28	152
Cusp forms	156	28	128
Eisenstein series	24	0	24

Trace form

28 * q - 4 * q^7 - 2 * q^9 - 4 * q^11 + q^13 - 4 * q^15 - 8 * q^17 - q^19 + 14 * q^21 + 8 * q^23 - 14 * q^25 - 13 * q^29 + 2 * q^31 - 25 * q^33 + 3 * q^35 - q^37 - 3 * q^39 - 8 * q^41 - 4 * q^43 - 38 * q^45 + 11 * q^47 + 24 * q^49 + 5 * q^51 + 52 * q^53 - q^57 - 8 * q^59 + 14 * q^61 - 21 * q^63 + 38 * q^65 + 14 * q^67 - 21 * q^69 - 12 * q^71 + 14 * q^73 - 14 * q^75 - 28 * q^77 + 5 * q^79 + 10 * q^81 + 9 * q^83 + 18 * q^85 + 18 * q^87 - 11 * q^89 - q^91 - 9 * q^93 + 28 * q^95 + 50 * q^97 - 29 * q^99

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.k.a	$468$	$2$	468.k	117.f	$3$	$28$	$14$	$3.737$		None		✓	✓	✓	468.2.j.a	$2$	$0$	$0$	$0$	$0$	$-4$		$\mathrm{SU}(2)[C_{3}]$

Decomposition of $S_{2}^{\mathrm{old}}(468, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(468, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(117, [\chi])$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(234, [\chi])$$^{\oplus 2}$