Space of modular forms of level 489, weight 2, and Character 489.q

• Label: 489.2.q
• Level: $489$
• Weight: $2$
• Character orbit: 489.q
• Rep. character: $\chi_{489}(4,\cdot)$
• Character field: $\Q(\zeta_{81})$
• Dimension: $1458$
• Newform subspaces: $2$
• Sturm bound: $109$
• Trace bound: $1$

Defining parameters

Level:	$N$	$=$	$489 = 3 \cdot 163$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	489.q (of order $81$ and degree $54$)
Character conductor:	$\operatorname{cond}(\chi)$	$=$	$163$
Character field:			$\Q(\zeta_{81})$
Newform subspaces:			$2$
Sturm bound:			$109$
Trace bound:			$1$
Distinguishing $T_p$:			$2$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(489, [\chi])$.

	Total	New	Old
Modular forms	3078	1458	1620
Cusp forms	2862	1458	1404
Eisenstein series	216	0	216

Trace form

1458 * q - 54 * q^23 - 54 * q^29 - 216 * q^32 - 216 * q^37 - 216 * q^46 - 216 * q^48 - 108 * q^49 - 108 * q^56 - 108 * q^62 - 54 * q^63 - 594 * q^70 - 108 * q^71 - 54 * q^73 - 594 * q^74 - 162 * q^80 - 216 * q^91 - 216 * q^95 - 162 * q^98

Decomposition of $S_{2}^{\mathrm{new}}(489, [\chi])$ 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
489.2.q.a	$489$	$2$	489.q	163.i	$81$	$702$	$13$	$3.905$		None		✓			489.2.q.a	$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{81}]$
489.2.q.b	$489$	$2$	489.q	163.i	$81$	$756$	$14$	$3.905$		None		✓	✓		489.2.q.b	$2$	$0$	$0$	$0$	$0$	$0$		$\mathrm{SU}(2)[C_{81}]$

Decomposition of $S_{2}^{\mathrm{old}}(489, [\chi])$ into lower level spaces

$S_{2}^{\mathrm{old}}(489, [\chi]) \simeq$ $S_{2}^{\mathrm{new}}(163, [\chi])$$^{\oplus 2}$