Space of modular forms of level 27, weight 2, and Character 27.e

• Label: 27.2.e
• Level: $27$
• Weight: $2$
• Character orbit: 27.e
• Rep. character: $\chi_{27}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $6$
• Trace bound: $0$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(27, [\chi])\).

	Total	New	Old
Modular forms	24	24	0
Cusp forms	12	12	0
Eisenstein series	12	12	0

Trace form

12 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 - 3 * q^5 - 6 * q^7 + 6 * q^8 - 3 * q^10 + 3 * q^11 + 12 * q^12 - 6 * q^13 + 15 * q^14 + 9 * q^15 + 9 * q^17 + 9 * q^18 - 3 * q^19 - 3 * q^20 - 12 * q^21 + 3 * q^22 - 12 * q^23 - 18 * q^24 + 3 * q^25 - 30 * q^26 - 9 * q^27 - 12 * q^28 - 6 * q^29 - 9 * q^30 + 3 * q^31 + 9 * q^34 + 12 * q^35 + 18 * q^36 - 3 * q^37 + 42 * q^38 + 33 * q^39 + 21 * q^40 + 15 * q^41 + 18 * q^42 + 3 * q^43 + 3 * q^44 - 9 * q^45 - 3 * q^46 - 15 * q^47 - 15 * q^48 + 12 * q^49 - 33 * q^50 - 18 * q^51 + 9 * q^52 - 18 * q^53 - 54 * q^54 - 12 * q^55 - 33 * q^56 - 3 * q^57 + 21 * q^58 - 12 * q^59 + 12 * q^61 - 12 * q^62 + 9 * q^63 + 12 * q^64 + 3 * q^65 - 9 * q^66 - 15 * q^67 + 9 * q^68 + 9 * q^69 - 15 * q^70 + 27 * q^71 + 18 * q^72 + 6 * q^73 + 33 * q^74 + 39 * q^75 - 48 * q^76 + 15 * q^77 + 18 * q^78 - 42 * q^79 + 42 * q^80 + 36 * q^81 - 12 * q^82 + 39 * q^83 + 6 * q^84 - 27 * q^85 + 51 * q^86 + 9 * q^87 - 30 * q^88 + 9 * q^89 + 18 * q^90 + 6 * q^91 - 39 * q^92 - 39 * q^93 - 15 * q^94 - 33 * q^95 + 3 * q^97 - 45 * q^98 - 27 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.2.e.a	$27$	$2$	27.e	27.e	$9$	$12$	$2$	$0.216$	12.0.\(\cdots\).1	None		✓	✓	✓	27.2.e.a	$2$	$0$	\(-6\)	\(-6\)	\(-3\)	\(-6\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(-1-\beta _{3}+\beta _{8})q^{2}+(-1-\beta _{2}+\beta _{6}+\cdots)q^{3}+\cdots\)