Space of modular forms of level 27, weight 7, and Character 27.d

• Label: 27.7.d
• Level: $27$
• Weight: $7$
• Character orbit: 27.d
• Rep. character: $\chi_{27}(8,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $10$
• Newform subspaces: $1$
• Sturm bound: $21$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
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:			\(21\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{7}(27, [\chi])\).

	Total	New	Old
Modular forms	42	14	28
Cusp forms	30	10	20
Eisenstein series	12	4	8

Trace form

\( 10 q + 3 q^{2} + 127 q^{4} + 219 q^{5} - 121 q^{7} + O(q^{10}) \)

Decomposition of \(S_{7}^{\mathrm{new}}(27, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.7.d.a	$27$	$7$	27.d	9.d	$6$	$10$	$5$	$6.211$	\(\mathbb{Q}[x]/(x^{10} - \cdots)\)	None		$2$	$0$	\(3\)	\(0\)	\(219\)	\(-121\)	$2^{2}\cdot 3^{14}$	$\mathrm{SU}(2)[C_{6}]$	\(q+\beta _{1}q^{2}+(\beta _{1}+\beta _{2}-5^{2}\beta _{4}+\beta _{5})q^{4}+\cdots\)

Decomposition of \(S_{7}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{7}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)