Space of modular forms of level 27, weight 5, and Character 27.d

• Label: 27.5.d
• Level: $27$
• Weight: $5$
• Character orbit: 27.d
• Rep. character: $\chi_{27}(8,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $15$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(15\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(27, [\chi])\).

	Total	New	Old
Modular forms	30	10	20
Cusp forms	18	6	12
Eisenstein series	12	4	8

Trace form

6 * q + 3 * q^2 + 15 * q^4 + 12 * q^5 + 12 * q^7 - 36 * q^10 - 483 * q^11 - 6 * q^13 + 1146 * q^14 + 15 * q^16 - 258 * q^19 - 1614 * q^20 - 369 * q^22 + 282 * q^23 - 273 * q^25 + 1308 * q^28 + 1056 * q^29 + 1290 * q^31 + 1161 * q^32 + 513 * q^34 + 12 * q^37 + 789 * q^38 - 1314 * q^40 - 7629 * q^41 - 285 * q^43 - 5760 * q^46 + 9642 * q^47 - 1863 * q^49 - 3027 * q^50 - 240 * q^52 + 2016 * q^55 + 462 * q^56 + 6462 * q^58 - 6225 * q^59 + 3630 * q^61 + 15450 * q^64 + 7158 * q^65 - 5055 * q^67 + 10503 * q^68 - 9684 * q^70 - 14622 * q^73 - 26454 * q^74 - 4047 * q^76 - 2580 * q^77 + 4764 * q^79 - 9702 * q^82 + 1866 * q^83 + 12366 * q^85 + 37731 * q^86 + 14787 * q^88 + 34836 * q^91 - 33636 * q^92 - 12708 * q^94 + 13362 * q^95 - 28959 * q^97

Decomposition of \(S_{5}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.5.d.a	$27$	$5$	27.d	9.d	$6$	$6$	$3$	$2.791$	6.0.39400128.1	None			✓	✓	9.5.d.a	$2$	$0$	\(3\)	\(0\)	\(12\)	\(12\)	$3^{4}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(4\beta _{1}+2\beta _{2}-\beta _{3}-3\beta _{4}+\cdots)q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

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