Space of modular forms of level 55, weight 4, and Character 55.l

• Label: 55.4.l
• Level: $55$
• Weight: $4$
• Character orbit: 55.l
• Rep. character: $\chi_{55}(2,\cdot)$
• Character field: $\Q(\zeta_{20})$
• Dimension: $128$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 55 = 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	55.l (of order \(20\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 55 \)
Character field:			\(\Q(\zeta_{20})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(55, [\chi])\).

	Total	New	Old
Modular forms	160	160	0
Cusp forms	128	128	0
Eisenstein series	32	32	0

Trace form

128 * q - 10 * q^2 - 10 * q^3 - 22 * q^5 - 20 * q^6 + 10 * q^7 - 10 * q^8 + 20 * q^11 - 460 * q^12 - 10 * q^13 + 254 * q^15 + 252 * q^16 + 310 * q^17 - 10 * q^18 - 704 * q^20 - 250 * q^22 + 560 * q^23 + 146 * q^25 - 676 * q^26 + 290 * q^27 - 730 * q^28 + 2030 * q^30 + 420 * q^31 - 1210 * q^33 - 10 * q^35 - 492 * q^36 + 690 * q^37 + 990 * q^38 - 650 * q^40 - 2240 * q^41 - 3370 * q^42 - 2308 * q^45 - 5180 * q^46 + 1910 * q^47 + 870 * q^48 + 1350 * q^50 + 2700 * q^51 + 8510 * q^52 + 1830 * q^53 + 2026 * q^55 + 8888 * q^56 + 2470 * q^57 + 30 * q^58 - 266 * q^60 + 460 * q^61 - 8040 * q^62 - 640 * q^63 + 1060 * q^66 - 7040 * q^67 - 5050 * q^68 - 2810 * q^70 + 1196 * q^71 - 5620 * q^72 + 7370 * q^73 - 5726 * q^75 + 850 * q^77 + 4860 * q^78 - 1962 * q^80 + 660 * q^81 + 5110 * q^82 - 6710 * q^83 - 170 * q^85 + 11084 * q^86 - 15490 * q^88 + 1180 * q^90 - 9896 * q^91 + 2340 * q^92 - 8450 * q^93 - 1390 * q^95 - 24960 * q^96 - 9210 * q^97

Decomposition of \(S_{4}^{\mathrm{new}}(55, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
55.4.l.a	$55$	$4$	55.l	55.l	$20$	$128$	$16$	$3.245$		None		✓	✓	✓	55.4.l.a	$4$	$0$	\(-10\)	\(-10\)	\(-22\)	\(10\)		$\mathrm{SU}(2)[C_{20}]$