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

• Label: 459.2.l
• Level: $459$
• Weight: $2$
• Character orbit: 459.l
• Rep. character: $\chi_{459}(298,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $96$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $19$

Defining parameters

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.l (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(19\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	240	96	144
Cusp forms	192	96	96
Eisenstein series	48	0	48

Trace form

96 * q - 32 * q^10 - 96 * q^16 + 16 * q^19 + 24 * q^22 + 32 * q^25 - 24 * q^28 - 8 * q^31 + 80 * q^34 - 48 * q^40 + 8 * q^43 - 72 * q^46 - 80 * q^49 - 32 * q^52 + 32 * q^58 + 24 * q^61 + 32 * q^67 + 48 * q^70 + 48 * q^73 + 80 * q^82 - 136 * q^85 - 80 * q^88 - 16 * q^91 - 56 * q^94 - 8 * q^97

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.l.a	$459$	$2$	459.l	17.d	$8$	$48$	$12$	$3.665$		None		✓			459.2.l.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$
459.2.l.b	$459$	$2$	459.l	17.d	$8$	$48$	$12$	$3.665$		None		✓			459.2.l.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$

Decomposition of \(S_{2}^{\mathrm{old}}(459, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(459, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(17, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(153, [\chi])\)\(^{\oplus 2}\)