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

• Label: 81.8.e
• Level: $81$
• Weight: $8$
• Character orbit: 81.e
• Rep. character: $\chi_{81}(10,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $120$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	81.e (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 27 \)
Character field:			\(\Q(\zeta_{9})\)
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	396	132	264
Cusp forms	360	120	240
Eisenstein series	36	12	24

Trace form

120 * q + 6 * q^2 - 6 * q^4 + 219 * q^5 - 6 * q^7 + 4611 * q^8 - 3 * q^10 - 9399 * q^11 - 6 * q^13 - 16647 * q^14 + 378 * q^16 + 58959 * q^17 - 3 * q^19 - 240243 * q^20 + 105762 * q^22 + 144084 * q^23 - 107997 * q^25 - 443202 * q^26 - 12 * q^28 - 107886 * q^29 + 297975 * q^31 + 639576 * q^32 - 265806 * q^34 + 450672 * q^35 - 3 * q^37 + 145596 * q^38 + 283521 * q^40 - 227085 * q^41 - 1080969 * q^43 + 1205115 * q^44 - 3 * q^46 + 5184339 * q^47 + 976008 * q^49 - 2324559 * q^50 - 3366135 * q^52 - 5631750 * q^53 - 12 * q^55 - 5254923 * q^56 + 3884295 * q^58 + 12534492 * q^59 + 3865440 * q^61 + 9923646 * q^62 - 10223619 * q^64 - 17158395 * q^65 + 5567061 * q^67 - 19858455 * q^68 - 1020993 * q^70 + 18563877 * q^71 + 3770934 * q^73 + 36278085 * q^74 - 1156998 * q^76 - 8471751 * q^77 + 16415526 * q^79 - 101080590 * q^80 - 12 * q^82 - 3147699 * q^83 - 7672131 * q^85 + 70854834 * q^86 - 34323078 * q^88 + 54647613 * q^89 + 3315066 * q^91 - 73858515 * q^92 + 22126539 * q^94 - 32541447 * q^95 + 41250117 * q^97 + 88493274 * q^98

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.e.a	$81$	$8$	81.e	27.e	$9$	$120$	$20$	$25.303$		None			✓	✓	27.8.e.a	$2$	$0$	\(6\)	\(0\)	\(219\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{8}^{\mathrm{old}}(81, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)