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

• Label: 459.2.p
• Level: $459$
• Weight: $2$
• Character orbit: 459.p
• Rep. character: $\chi_{459}(80,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $192$
• Newform subspaces: $2$
• Sturm bound: $108$
• Trace bound: $28$

Defining parameters

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.p (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 51 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(108\)
Trace bound:			\(28\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	480	192	288
Cusp forms	384	192	192
Eisenstein series	96	0	96

Trace form

192 * q - 64 * q^25 + 48 * q^28 + 32 * q^31 - 128 * q^34 + 32 * q^37 + 32 * q^40 - 16 * q^43 - 16 * q^46 - 32 * q^49 - 64 * q^52 - 32 * q^55 - 32 * q^58 - 16 * q^61 - 32 * q^64 + 32 * q^70 - 128 * q^73 + 64 * q^76 + 32 * q^79 - 64 * q^82 + 16 * q^85 + 32 * q^88 - 64 * q^91 - 32 * q^94

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.p.a	$459$	$2$	459.p	51.i	$16$	$96$	$12$	$3.665$		None		✓			459.2.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
459.2.p.b	$459$	$2$	459.p	51.i	$16$	$96$	$12$	$3.665$		None		✓			459.2.p.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

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

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