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

• Label: 3.27.b
• Level: $3$
• Weight: $27$
• Character orbit: 3.b
• Rep. character: $\chi_{3}(2,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	10	10	0
Cusp forms	8	8	0
Eisenstein series	2	2	0

Trace form

\( 8 q - 1261080 q^{3} - 248848672 q^{4} + 4268261088 q^{6} - 83723264240 q^{7} + 3535237525320 q^{9} + O(q^{10}) \)

Decomposition of \(S_{27}^{\mathrm{new}}(3, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3.27.b.a	$3$	$27$	3.b	3.b	$2$	$8$	$8$	$12.849$	\(\mathbb{Q}[x]/(x^{8} + \cdots)\)	None		$2$	$0$	\(0\)	\(-1261080\)	\(0\)	\(-83723264240\)	$2^{33}\cdot 3^{38}\cdot 5^{3}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-157635-5\beta _{1}-\beta _{2}+\cdots)q^{3}+\cdots\)