Space of modular forms of level 81, weight 8, and Character 81.g

• Label: 81.8.g
• Level: $81$
• Weight: $8$
• Character orbit: 81.g
• Rep. character: $\chi_{81}(4,\cdot)$
• Character field: $\Q(\zeta_{27})$
• Dimension: $1116$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	81.g (of order \(27\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{27})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(81, [\chi])\).

	Total	New	Old
Modular forms	1152	1152	0
Cusp forms	1116	1116	0
Eisenstein series	36	36	0

Trace form

1116 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 18 * q^5 - 18 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 18 * q^10 - 18 * q^11 - 18 * q^12 - 18 * q^13 - 18 * q^14 - 18 * q^15 - 18 * q^16 - 18 * q^17 + 108774 * q^18 - 18 * q^19 - 163602 * q^20 + 185985 * q^21 - 18 * q^22 + 210933 * q^23 - 100242 * q^24 - 18 * q^25 - 949113 * q^26 - 416979 * q^27 - 9 * q^28 + 270225 * q^29 + 1355166 * q^30 - 18 * q^31 + 1496430 * q^32 + 154233 * q^33 - 18 * q^34 - 1735011 * q^35 - 2486034 * q^36 - 18 * q^37 + 2149974 * q^38 - 18 * q^39 - 18 * q^40 + 2134188 * q^41 - 4341303 * q^42 - 18 * q^43 - 4051242 * q^44 + 1459008 * q^45 - 18 * q^46 + 6232500 * q^47 + 9962649 * q^48 - 18 * q^49 - 1113975 * q^50 - 4677327 * q^51 + 1134 * q^52 - 8039367 * q^53 - 17669880 * q^54 - 9 * q^55 - 3554964 * q^56 + 3123720 * q^57 - 18 * q^58 + 13283721 * q^59 + 28050615 * q^60 - 18 * q^61 + 12611295 * q^62 - 1006956 * q^63 - 18 * q^64 - 33580332 * q^65 - 11249946 * q^66 - 13231179 * q^67 + 53101719 * q^68 + 31645980 * q^69 + 5237982 * q^70 - 21189690 * q^71 - 87478290 * q^72 - 18 * q^73 - 49640850 * q^74 - 18281268 * q^75 + 1809198 * q^76 + 24022494 * q^77 + 48218193 * q^78 - 24623316 * q^79 + 129023964 * q^80 + 35458470 * q^81 - 36 * q^82 + 16752006 * q^83 + 4745169 * q^84 + 11859732 * q^85 - 64923282 * q^86 - 92159586 * q^87 + 60922350 * q^88 - 14312295 * q^89 - 99084321 * q^90 - 18 * q^91 - 108457200 * q^92 - 51873804 * q^93 - 52133346 * q^94 + 104024754 * q^95 + 241882443 * q^96 - 26124759 * q^97 + 156522699 * q^98 + 10370646 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(81, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
81.8.g.a	$81$	$8$	81.g	81.g	$27$	$1116$	$62$	$25.303$		None		✓	✓	✓	81.8.g.a	$2$	$0$	\(-18\)	\(-18\)	\(-18\)	\(-18\)		$\mathrm{SU}(2)[C_{27}]$