Space of modular forms of level 81, weight 12, and Character 81.e

• Label: 81.12.e
• Level: $81$
• Weight: $12$
• Character orbit: 81.e
• Rep. character: $\chi_{81}(10,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $192$
• Newform subspaces: $1$
• Sturm bound: $108$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 12 \)
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:			\(108\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(81, [\chi])\).

	Total	New	Old
Modular forms	612	204	408
Cusp forms	576	192	384
Eisenstein series	36	12	24

Trace form

192 * q + 6 * q^2 - 6 * q^4 - 2931 * q^5 - 6 * q^7 + 294915 * q^8 - 3 * q^10 + 1594293 * q^11 - 6 * q^13 - 5263143 * q^14 + 6138 * q^16 + 17038287 * q^17 - 3 * q^19 - 33966483 * q^20 - 6811494 * q^22 + 154612956 * q^23 - 39922647 * q^25 - 72169026 * q^26 - 12 * q^28 + 818363742 * q^29 - 114913365 * q^31 - 2449907208 * q^32 + 250353882 * q^34 + 1986199152 * q^35 - 3 * q^37 + 199328700 * q^38 + 159067281 * q^40 - 2363326233 * q^41 + 2031687507 * q^43 + 6781787259 * q^44 - 3 * q^46 - 1321238505 * q^47 + 5300190696 * q^49 + 19347232641 * q^50 - 7435159623 * q^52 - 7067989026 * q^53 - 12 * q^55 + 8014324821 * q^56 + 16115317383 * q^58 - 21931606932 * q^59 - 16510964208 * q^61 - 11823393570 * q^62 - 80530636803 * q^64 - 4275338385 * q^65 - 38080922415 * q^67 - 82368304983 * q^68 + 60497186367 * q^70 + 50263647093 * q^71 + 1424119740 * q^73 + 72634311813 * q^74 - 116456331270 * q^76 - 62223517041 * q^77 + 90355950390 * q^79 - 24737530830 * q^80 - 12 * q^82 - 113535448779 * q^83 - 164592103131 * q^85 + 28905145338 * q^86 + 67619592186 * q^88 + 100969659531 * q^89 - 61084040502 * q^91 + 29835580269 * q^92 - 264765665733 * q^94 - 349741980687 * q^95 - 109680687051 * q^97 - 282639387726 * q^98

Decomposition of \(S_{12}^{\mathrm{new}}(81, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
81.12.e.a	$81$	$12$	81.e	27.e	$9$	$192$	$32$	$62.236$		None			✓	✓	27.12.e.a	$2$	$0$	\(6\)	\(0\)	\(-2931\)	\(-6\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{12}^{\mathrm{old}}(81, [\chi])\) into lower level spaces

\( S_{12}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{12}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)