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

• Label: 81.5.b
• Level: $81$
• Weight: $5$
• Character orbit: 81.b
• Rep. character: $\chi_{81}(80,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $2$
• Sturm bound: $45$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(45\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	42	18	24
Cusp forms	30	14	16
Eisenstein series	12	4	8

Trace form

14 * q - 94 * q^4 + 28 * q^7 + 156 * q^10 - 248 * q^13 + 110 * q^16 - 566 * q^19 + 1878 * q^22 - 1126 * q^25 - 944 * q^28 + 364 * q^31 + 2502 * q^34 + 4600 * q^37 - 8580 * q^40 - 3266 * q^43 - 2364 * q^46 + 7158 * q^49 + 6880 * q^52 - 8196 * q^55 - 1776 * q^58 - 10736 * q^61 + 15458 * q^64 - 3398 * q^67 - 228 * q^70 + 1954 * q^73 + 35506 * q^76 + 31348 * q^79 - 42522 * q^82 - 24048 * q^85 - 62466 * q^88 + 21752 * q^91 - 30216 * q^94 + 30430 * q^97

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.b.a	$81$	$5$	81.b	3.b	$2$	$6$	$6$	$8.373$	6.0.39400128.1	None					9.5.d.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-24\)	$2^{3}\cdot 3^{9}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-5+\beta _{2})q^{4}+\beta _{4}q^{5}+(-4+\cdots)q^{7}+\cdots\)
81.5.b.b	$81$	$5$	81.b	3.b	$2$	$8$	$8$	$8.373$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		✓	✓		81.5.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(52\)	$3^{18}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-8+\beta _{5})q^{4}+(\beta _{1}-\beta _{4}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(81, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(81, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{5}^{\mathrm{new}}(27, [\chi])\)\(^{\oplus 2}\)