Space of modular forms of level 81, weight 5, and Character 81.h

• Label: 81.5.h
• Level: $81$
• Weight: $5$
• Character orbit: 81.h
• Rep. character: $\chi_{81}(2,\cdot)$
• Character field: $\Q(\zeta_{54})$
• Dimension: $630$
• Newform subspaces: $1$
• Sturm bound: $45$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(45\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(81, [\chi])\).

	Total	New	Old
Modular forms	666	666	0
Cusp forms	630	630	0
Eisenstein series	36	36	0

Trace form

630 * 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 - 2034 * q^18 - 18 * q^19 + 846 * q^20 + 2277 * q^21 - 18 * q^22 + 2979 * q^23 + 4734 * q^24 - 18 * q^25 - 27 * q^26 - 1449 * q^27 - 9 * q^28 - 3987 * q^29 - 9522 * q^30 - 18 * q^31 - 9090 * q^32 - 3231 * q^33 - 18 * q^34 + 2655 * q^35 + 10062 * q^36 - 18 * q^37 + 7326 * q^38 - 18 * q^39 - 18 * q^40 - 13410 * q^41 - 18333 * q^42 - 18 * q^43 + 4518 * q^44 + 11214 * q^45 - 18 * q^46 + 18774 * q^47 + 35127 * q^48 - 18 * q^49 + 31923 * q^50 + 12330 * q^51 - 162 * q^52 - 27 * q^53 - 13500 * q^54 - 9 * q^55 - 38808 * q^56 - 21186 * q^57 - 18 * q^58 - 31014 * q^59 - 58167 * q^60 - 18 * q^61 - 38331 * q^62 - 14058 * q^63 - 18 * q^64 + 60354 * q^65 + 99126 * q^66 - 12303 * q^67 + 72153 * q^68 + 20502 * q^69 + 21582 * q^70 - 39546 * q^71 - 138258 * q^72 - 18 * q^73 - 96786 * q^74 - 56268 * q^75 + 44046 * q^76 - 62658 * q^77 - 44523 * q^78 + 8460 * q^79 + 11574 * q^81 - 36 * q^82 + 33894 * q^83 + 153927 * q^84 - 39168 * q^85 + 117486 * q^86 + 125982 * q^87 - 72594 * q^88 + 7596 * q^89 - 1557 * q^90 - 18 * q^91 + 48312 * q^92 + 3294 * q^93 + 6030 * q^94 + 21798 * q^95 - 37665 * q^96 + 43587 * q^97 + 11079 * q^98 + 4266 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(81, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
81.5.h.a	$81$	$5$	81.h	81.h	$54$	$630$	$35$	$8.373$		None		✓	✓	✓	81.5.h.a	$2$	$0$	\(-18\)	\(-18\)	\(-18\)	\(-18\)		$\mathrm{SU}(2)[C_{54}]$