Space of modular forms of level 81, weight 9, and Character 81.h

• Label: 81.9.h
• Level: $81$
• Weight: $9$
• Character orbit: 81.h
• Rep. character: $\chi_{81}(2,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $1278$
• Newform subspaces: $1$
• Sturm bound: $81$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	81.h (of order \(54\) and degree \(18\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 81 \)
Character field:			\(\Q(\zeta_{54})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(81\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(81, [\chi])\).

	Total	New	Old
Modular forms	1314	1314	0
Cusp forms	1278	1278	0
Eisenstein series	36	36	0

Trace form

1278 * 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 - 274194 * q^18 - 18 * q^19 - 677394 * q^20 - 1360953 * q^21 - 18 * q^22 + 932049 * q^23 + 3725550 * q^24 - 18 * q^25 - 27 * q^26 - 1933299 * q^27 - 9 * q^28 - 2853729 * q^29 - 1292562 * q^30 - 18 * q^31 + 11466990 * q^32 + 6069339 * q^33 - 18 * q^34 - 6225435 * q^35 - 18224658 * q^36 - 18 * q^37 + 12749166 * q^38 - 18 * q^39 - 18 * q^40 - 6454962 * q^41 + 39542067 * q^42 - 18 * q^43 - 17341146 * q^44 - 37896786 * q^45 - 18 * q^46 - 19806786 * q^47 + 15217767 * q^48 - 18 * q^49 + 104798403 * q^50 + 54355878 * q^51 - 2322 * q^52 - 27 * q^53 - 75728412 * q^54 - 9 * q^55 - 168854472 * q^56 - 65747826 * q^57 - 18 * q^58 + 7377030 * q^59 + 125543673 * q^60 - 18 * q^61 + 223709589 * q^62 + 101958462 * q^63 - 18 * q^64 - 45382806 * q^65 - 552090186 * q^66 + 95245587 * q^67 - 190809207 * q^68 + 273910662 * q^69 - 177120018 * q^70 + 251437590 * q^71 + 548536302 * q^72 - 18 * q^73 - 154054674 * q^74 - 246093768 * q^75 + 305980398 * q^76 - 574220898 * q^77 - 478793403 * q^78 + 103151808 * q^79 + 148365990 * q^81 - 36 * q^82 + 368657334 * q^83 + 1377777303 * q^84 - 257411268 * q^85 + 435234798 * q^86 + 61361982 * q^87 + 213663726 * q^88 - 893853972 * q^89 - 624764277 * q^90 - 18 * q^91 - 745285608 * q^92 - 53952426 * q^93 - 106493202 * q^94 - 313936362 * q^95 + 626058639 * q^96 - 427023783 * q^97 - 590433561 * q^98 - 967332078 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(81, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
81.9.h.a	$81$	$9$	81.h	81.h	$54$	$1278$	$71$	$32.998$		None		✓	✓	✓	81.9.h.a	$2$	$0$	\(-18\)	\(-18\)	\(-18\)	\(-18\)		$\mathrm{SU}(2)[C_{54}]$