Space of modular forms of level 558, weight 2, and Character 558.h

• Label: 558.2.h
• Level: $558$
• Weight: $2$
• Character orbit: 558.h
• Rep. character: $\chi_{558}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $64$
• Newform subspaces: $2$
• Sturm bound: $192$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 558 = 2 \cdot 3^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	558.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 279 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(192\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(558, [\chi])\).

	Total	New	Old
Modular forms	200	64	136
Cusp forms	184	64	120
Eisenstein series	16	0	16

Trace form

64 * q - 4 * q^3 - 32 * q^4 + 4 * q^5 - 4 * q^7 - 4 * q^9 - 4 * q^11 + 8 * q^12 + 8 * q^13 - 2 * q^15 - 32 * q^16 - 8 * q^17 + 16 * q^18 - 4 * q^19 - 2 * q^20 - 8 * q^21 - 2 * q^23 + 76 * q^25 - 16 * q^26 + 20 * q^27 + 2 * q^28 - 12 * q^29 + 30 * q^30 + 4 * q^31 + 6 * q^33 + 12 * q^35 - 4 * q^36 - 10 * q^37 - 24 * q^38 - 8 * q^39 - 40 * q^41 + 10 * q^42 - 4 * q^43 - 4 * q^44 - 12 * q^47 - 4 * q^48 + 60 * q^49 - 50 * q^51 - 4 * q^52 - 14 * q^53 - 24 * q^54 - 6 * q^57 + 6 * q^58 - 18 * q^59 + 4 * q^60 + 14 * q^61 + 12 * q^62 - 40 * q^63 + 64 * q^64 + 32 * q^65 + 16 * q^66 - 16 * q^67 - 8 * q^68 - 42 * q^69 + 6 * q^70 + 14 * q^71 - 8 * q^72 + 14 * q^73 + 56 * q^74 + 18 * q^75 - 4 * q^76 + 4 * q^77 - 38 * q^78 + 20 * q^79 - 2 * q^80 - 4 * q^81 + 28 * q^83 - 2 * q^84 - 28 * q^86 - 20 * q^89 - 14 * q^90 - 32 * q^91 - 2 * q^92 + 6 * q^93 + 30 * q^95 - 4 * q^97 + 4 * q^98 - 28 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(558, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
558.2.h.a	$558$	$2$	558.h	279.g	$3$	$32$	$16$	$4.456$		None		✓			558.2.g.a	$2$	$0$	\(-16\)	\(-2\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{3}]$
558.2.h.b	$558$	$2$	558.h	279.g	$3$	$32$	$16$	$4.456$		None		✓			558.2.g.b	$2$	$0$	\(16\)	\(-2\)	\(2\)	\(-2\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{2}^{\mathrm{old}}(558, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(558, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(279, [\chi])\)\(^{\oplus 2}\)