Space of modular forms of level 544, weight 2, and Character 544.z

• Label: 544.2.z
• Level: $544$
• Weight: $2$
• Character orbit: 544.z
• Rep. character: $\chi_{544}(13,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $280$
• Newform subspaces: $1$
• Sturm bound: $144$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 544 = 2^{5} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	544.z (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 544 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(144\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(544, [\chi])\).

	Total	New	Old
Modular forms	296	296	0
Cusp forms	280	280	0
Eisenstein series	16	16	0

Trace form

280 * q - 4 * q^3 - 8 * q^4 - 4 * q^5 - 4 * q^6 - 12 * q^10 - 4 * q^11 - 4 * q^12 - 8 * q^13 + 20 * q^14 + 32 * q^15 - 8 * q^16 - 8 * q^18 - 20 * q^20 - 8 * q^21 - 28 * q^22 - 8 * q^23 - 16 * q^24 + 8 * q^27 + 8 * q^28 - 4 * q^29 + 16 * q^30 - 8 * q^31 + 40 * q^32 - 16 * q^33 + 28 * q^34 - 8 * q^35 - 4 * q^37 - 8 * q^38 - 8 * q^39 + 28 * q^40 - 8 * q^41 + 48 * q^42 - 48 * q^44 + 4 * q^45 + 8 * q^46 + 80 * q^48 - 232 * q^49 - 8 * q^50 - 4 * q^51 + 40 * q^52 - 60 * q^54 - 8 * q^55 + 52 * q^56 - 64 * q^58 - 40 * q^60 + 28 * q^61 + 28 * q^62 - 8 * q^63 + 40 * q^64 - 8 * q^65 - 8 * q^67 - 40 * q^68 - 72 * q^69 + 24 * q^70 - 72 * q^71 - 8 * q^72 - 124 * q^74 - 36 * q^75 + 56 * q^77 + 16 * q^78 + 60 * q^80 - 52 * q^82 - 8 * q^84 - 36 * q^85 - 8 * q^86 + 60 * q^88 - 8 * q^89 - 56 * q^90 + 8 * q^91 + 32 * q^92 - 8 * q^95 + 64 * q^96 - 8 * q^97 - 160 * q^98 - 52 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(544, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
544.2.z.a	$544$	$2$	544.z	544.z	$8$	$280$	$70$	$4.344$		None		✓	✓	✓	544.2.z.a	$2$	$0$	\(0\)	\(-4\)	\(-4\)	\(0\)		$\mathrm{SU}(2)[C_{8}]$