Space of modular forms of level 27, weight 11, and Character 27.f

• Label: 27.11.f
• Level: $27$
• Weight: $11$
• Character orbit: 27.f
• Rep. character: $\chi_{27}(2,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $174$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	27.f (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(27, [\chi])\).

	Total	New	Old
Modular forms	186	186	0
Cusp forms	174	174	0
Eisenstein series	12	12	0

Trace form

174 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 4965 * q^5 + 18234 * q^6 - 6 * q^7 - 9 * q^8 + 119124 * q^9 - 3 * q^10 - 978 * q^11 - 1015107 * q^12 - 6 * q^13 + 2134569 * q^14 - 2548539 * q^15 - 3078 * q^16 - 9 * q^17 + 6676947 * q^18 - 3 * q^19 + 15925353 * q^20 - 21049824 * q^21 + 10420410 * q^22 + 8437692 * q^23 + 87359400 * q^24 - 14881965 * q^25 - 60562494 * q^27 - 12 * q^28 + 7820868 * q^29 + 216153117 * q^30 - 51711531 * q^31 + 76244832 * q^32 - 198927081 * q^33 + 92236410 * q^34 - 260153622 * q^35 + 199074744 * q^36 - 3 * q^37 + 250645020 * q^38 + 152777949 * q^39 - 26151153 * q^40 - 837714012 * q^41 - 1627952634 * q^42 - 213300456 * q^43 + 2245906431 * q^44 + 1041263847 * q^45 - 3 * q^46 - 1685998563 * q^47 - 1664196711 * q^48 - 183168366 * q^49 + 2548576023 * q^50 + 1007158626 * q^51 - 912655665 * q^52 - 1206704682 * q^54 - 12 * q^55 - 4260806997 * q^56 - 1000586442 * q^57 - 496853331 * q^58 + 1806342150 * q^59 + 1176655374 * q^60 - 1784159286 * q^61 + 2786630112 * q^62 + 2270781765 * q^63 + 8858370045 * q^64 - 2961878001 * q^65 - 5594499243 * q^66 - 915608058 * q^67 + 11412166995 * q^68 - 7767764199 * q^69 + 1945422669 * q^70 - 5512912173 * q^71 - 15991303644 * q^72 + 2110132140 * q^73 + 22008588729 * q^74 + 15296936925 * q^75 + 11875694586 * q^76 - 2702962221 * q^77 - 12511026108 * q^78 + 6660721974 * q^79 + 440880768 * q^81 - 12 * q^82 + 7670489421 * q^83 - 31766160684 * q^84 - 6965484381 * q^85 - 33241766118 * q^86 - 10927113525 * q^87 + 28790289402 * q^88 + 34430237370 * q^89 + 12602186028 * q^90 - 991980102 * q^91 + 40280154009 * q^92 + 57140838285 * q^93 - 62587945905 * q^94 - 12104972679 * q^95 - 78182924274 * q^96 + 48297833958 * q^97 - 103117506282 * q^98 - 72892391589 * q^99

Decomposition of \(S_{11}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.11.f.a	$27$	$11$	27.f	27.f	$18$	$174$	$29$	$17.155$		None		✓	✓	✓	27.11.f.a	$2$	$0$	\(-6\)	\(-6\)	\(-4965\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$