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

• Label: 459.2.e
• Level: $459$
• Weight: $2$
• Character orbit: 459.e
• Rep. character: $\chi_{459}(154,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $108$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 459 = 3^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	459.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(108\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	120	32	88
Cusp forms	96	32	64
Eisenstein series	24	0	24

Trace form

32 * q - 16 * q^4 + 2 * q^5 - 2 * q^7 + 12 * q^8 + 8 * q^11 - 2 * q^13 + 4 * q^14 - 16 * q^16 - 8 * q^17 + 4 * q^19 - 10 * q^20 + 8 * q^23 - 10 * q^25 + 16 * q^26 + 16 * q^28 - 6 * q^29 - 2 * q^31 - 22 * q^32 + 20 * q^35 - 8 * q^37 - 4 * q^38 + 12 * q^41 - 8 * q^43 - 60 * q^44 - 24 * q^46 + 4 * q^47 - 6 * q^49 - 4 * q^50 + 10 * q^52 + 8 * q^53 + 12 * q^55 + 24 * q^56 + 6 * q^58 - 24 * q^59 - 2 * q^61 - 108 * q^62 - 4 * q^64 - 20 * q^65 - 8 * q^67 + 12 * q^68 - 4 * q^71 + 28 * q^73 + 46 * q^74 - 8 * q^76 - 24 * q^77 - 14 * q^79 + 148 * q^80 - 36 * q^82 - 30 * q^83 - 38 * q^86 - 24 * q^88 + 56 * q^89 + 44 * q^91 - 4 * q^92 + 6 * q^94 + 64 * q^95 + 4 * q^97 - 92 * q^98

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.e.a	$459$	$2$	459.e	9.c	$3$	$4$	$2$	$3.665$	\(\Q(\sqrt{-3}, \sqrt{5})\)	None					153.2.e.a	$2$	$0$	\(1\)	\(0\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-\beta _{3})q^{4}+(-2\beta _{1}+\cdots)q^{5}+\cdots\)
459.2.e.b	$459$	$2$	459.e	9.c	$3$	$8$	$4$	$3.665$	8.0.152695449.1	None					153.2.e.b	$2$	$0$	\(-1\)	\(0\)	\(1\)	\(3\)	$3^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{2}-\beta _{3})q^{2}+(-1-\beta _{1}-\beta _{4}+\cdots)q^{4}+\cdots\)
459.2.e.c	$459$	$2$	459.e	9.c	$3$	$20$	$10$	$3.665$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None			✓		153.2.e.c	$2$	$0$	\(0\)	\(0\)	\(1\)	\(-11\)	$3^{7}$	$\mathrm{SU}(2)[C_{3}]$	\(q-\beta _{16}q^{2}+(-\beta _{1}-\beta _{7})q^{4}-\beta _{14}q^{5}+\cdots\)

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

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