Space of modular forms of level 27, weight 3, and Character 27.b

• Label: 27.3.b
• Level: $27$
• Weight: $3$
• Character orbit: 27.b
• Rep. character: $\chi_{27}(26,\cdot)$
• Character field: $\Q$
• Dimension: $3$
• Newform subspaces: $2$
• Sturm bound: $9$
• Trace bound: $1$

Defining parameters

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

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(27, [\chi])\).

	Total	New	Old
Modular forms	9	3	6
Cusp forms	3	3	0
Eisenstein series	6	0	6

Trace form

3 * q - 6 * q^4 - 3 * q^7 + 18 * q^10 - 21 * q^13 - 6 * q^16 - 21 * q^19 + 90 * q^22 + 57 * q^25 - 102 * q^28 - 48 * q^31 - 108 * q^34 + 87 * q^37 - 18 * q^40 + 78 * q^43 + 72 * q^46 + 72 * q^49 + 96 * q^52 - 90 * q^55 - 180 * q^58 - 273 * q^61 + 246 * q^64 - 129 * q^67 + 90 * q^70 + 33 * q^73 + 204 * q^76 + 159 * q^79 - 360 * q^82 + 108 * q^85 - 90 * q^88 - 87 * q^91 + 36 * q^94 - 3 * q^97

Decomposition of \(S_{3}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.3.b.a	$27$	$3$	27.b	3.b	$2$	$1$	$1$	$0.736$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	✓			27.3.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(-13\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+4q^{4}-13q^{7}-q^{13}+2^{4}q^{16}+11q^{19}+\cdots\)
27.3.b.b	$27$	$3$	27.b	3.b	$2$	$2$	$2$	$0.736$	\(\Q(\sqrt{-1}) \)	None		✓	✓		27.3.b.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(10\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-5 q^{4}-\beta q^{5}+5 q^{7}-\beta q^{8}+\cdots\)