Space of modular forms of level 27, weight 11, and Character 27.d

• Label: 27.11.d
• Level: $27$
• Weight: $11$
• Character orbit: 27.d
• Rep. character: $\chi_{27}(8,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $18$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	27.d (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{11}(27, [\chi])\).

	Total	New	Old
Modular forms	66	22	44
Cusp forms	54	18	36
Eisenstein series	12	4	8

Trace form

18 * q + 3 * q^2 + 4095 * q^4 - 4956 * q^5 - 6120 * q^7 - 2052 * q^10 - 969 * q^11 + 140274 * q^13 + 2134578 * q^14 - 1571841 * q^16 + 2771370 * q^19 - 14542734 * q^20 - 3475521 * q^22 + 9944382 * q^23 + 14726277 * q^25 - 22968324 * q^28 + 41383956 * q^29 + 28428390 * q^31 - 165205143 * q^32 - 66263103 * q^34 + 63695196 * q^37 + 621662181 * q^38 - 75566250 * q^40 - 452543883 * q^41 + 102086037 * q^43 + 44251488 * q^46 + 289445970 * q^47 + 6735231 * q^49 - 1915252779 * q^50 + 19035576 * q^52 - 289455552 * q^55 + 4272894318 * q^56 - 83900178 * q^58 - 3065773551 * q^59 + 141349086 * q^61 - 28980486 * q^64 + 11094862926 * q^65 + 954074115 * q^67 - 21469701105 * q^68 - 1440686628 * q^70 + 772009902 * q^73 + 30101814978 * q^74 - 40906287 * q^76 - 25001072268 * q^77 + 2079634212 * q^79 - 1423292742 * q^82 + 23396438442 * q^83 - 5975304714 * q^85 - 39111097821 * q^86 + 2974531059 * q^88 + 2180413260 * q^91 + 40885098684 * q^92 + 6395997924 * q^94 - 22335455946 * q^95 - 14510723337 * q^97

Decomposition of \(S_{11}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.11.d.a	$27$	$11$	27.d	9.d	$6$	$18$	$9$	$17.155$	\(\mathbb{Q}[x]/(x^{18} - \cdots)\)	None			✓	✓	9.11.d.a	$2$	$0$	\(3\)	\(0\)	\(-4956\)	\(-6120\)	$2^{14}\cdot 3^{52}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{2}q^{2}+(454-454\beta _{1}+2\beta _{2}+2\beta _{3}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{11}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{11}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{11}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)