Space of modular forms of level 459, weight 2, and Character 459.x

• Label: 459.2.x
• Level: $459$
• Weight: $2$
• Character orbit: 459.x
• Rep. character: $\chi_{459}(4,\cdot)$
• Character field: $\Q(\zeta_{36})$
• Dimension: $624$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.x (of order \(36\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 459 \)
Character field:			\(\Q(\zeta_{36})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(459, [\chi])\).

	Total	New	Old
Modular forms	672	672	0
Cusp forms	624	624	0
Eisenstein series	48	48	0

Trace form

624 * q - 12 * q^3 - 24 * q^4 - 12 * q^5 - 12 * q^6 - 12 * q^7 - 6 * q^10 - 18 * q^11 + 6 * q^12 - 24 * q^13 - 42 * q^14 - 48 * q^16 - 6 * q^17 - 24 * q^18 - 24 * q^20 - 120 * q^21 - 30 * q^22 - 48 * q^23 - 18 * q^27 - 24 * q^28 - 12 * q^29 - 24 * q^30 - 12 * q^31 + 48 * q^33 - 42 * q^34 + 84 * q^35 - 6 * q^37 - 72 * q^38 - 60 * q^39 - 18 * q^40 - 78 * q^41 - 6 * q^44 - 42 * q^45 - 6 * q^46 + 36 * q^47 - 48 * q^48 - 24 * q^50 + 72 * q^51 + 24 * q^52 + 24 * q^54 - 48 * q^55 + 30 * q^56 + 18 * q^57 - 12 * q^58 - 12 * q^61 - 6 * q^62 - 186 * q^63 + 216 * q^64 - 78 * q^65 - 24 * q^67 + 72 * q^68 + 144 * q^69 - 30 * q^71 - 120 * q^72 - 6 * q^73 + 24 * q^74 - 48 * q^75 - 72 * q^78 + 60 * q^79 - 300 * q^80 - 24 * q^82 - 24 * q^84 - 12 * q^85 + 228 * q^86 - 180 * q^88 - 156 * q^89 + 48 * q^90 - 6 * q^91 - 210 * q^92 + 114 * q^95 - 132 * q^96 + 42 * q^97 - 96 * q^98 + 156 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(459, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
459.2.x.a	$459$	$2$	459.x	459.x	$36$	$624$	$52$	$3.665$		None		✓	✓	✓	459.2.x.a	$4$	$0$	\(0\)	\(-12\)	\(-12\)	\(-12\)		$\mathrm{SU}(2)[C_{36}]$