Space of modular forms of level 27, weight 8, and Character 27.e

• Label: 27.8.e
• Level: $27$
• Weight: $8$
• Character orbit: 27.e
• Rep. character: $\chi_{27}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(27, [\chi])\).

	Total	New	Old
Modular forms	132	132	0
Cusp forms	120	120	0
Eisenstein series	12	12	0

Trace form

120 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 219 * q^5 + 1386 * q^6 - 6 * q^7 - 4611 * q^8 - 1728 * q^9 - 3 * q^10 + 9399 * q^11 - 10545 * q^12 - 6 * q^13 + 16647 * q^14 + 11709 * q^15 + 378 * q^16 - 58959 * q^17 - 156051 * q^18 - 3 * q^19 + 240243 * q^20 - 516 * q^21 + 105762 * q^22 - 144084 * q^23 - 150894 * q^24 - 107997 * q^25 + 443202 * q^26 + 114363 * q^27 - 12 * q^28 + 107886 * q^29 - 179901 * q^30 + 297975 * q^31 - 639576 * q^32 - 31338 * q^33 - 265806 * q^34 - 450672 * q^35 + 51264 * q^36 - 3 * q^37 - 145596 * q^38 + 1919661 * q^39 + 283521 * q^40 + 227085 * q^41 + 3792042 * q^42 - 1080969 * q^43 - 1205115 * q^44 - 4430925 * q^45 - 3 * q^46 - 5184339 * q^47 - 2424039 * q^48 + 976008 * q^49 + 2324559 * q^50 + 2918034 * q^51 - 3366135 * q^52 + 5631750 * q^53 + 11971422 * q^54 - 12 * q^55 + 5254923 * q^56 - 284637 * q^57 + 3884295 * q^58 - 12534492 * q^59 - 29390886 * q^60 + 3865440 * q^61 - 9923646 * q^62 + 3292389 * q^63 - 10223619 * q^64 + 17158395 * q^65 + 39100653 * q^66 + 5567061 * q^67 + 19858455 * q^68 - 12682935 * q^69 - 1020993 * q^70 - 18563877 * q^71 - 33138540 * q^72 + 3770934 * q^73 - 36278085 * q^74 - 26317941 * q^75 - 1156998 * q^76 + 8471751 * q^77 + 36593658 * q^78 + 16415526 * q^79 + 101080590 * q^80 + 45736524 * q^81 - 12 * q^82 + 3147699 * q^83 - 27588054 * q^84 - 7672131 * q^85 - 70854834 * q^86 - 55384731 * q^87 - 34323078 * q^88 - 54647613 * q^89 - 25256970 * q^90 + 3315066 * q^91 + 73858515 * q^92 + 69808065 * q^93 + 22126539 * q^94 + 32541447 * q^95 + 33014034 * q^96 + 41250117 * q^97 - 88493274 * q^98 - 111262167 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.8.e.a	$27$	$8$	27.e	27.e	$9$	$120$	$20$	$8.434$		None		✓	✓	✓	27.8.e.a	$2$	$0$	\(-6\)	\(-6\)	\(-219\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$