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

• Label: 27.7.b
• Level: $27$
• Weight: $7$
• Character orbit: 27.b
• Rep. character: $\chi_{27}(26,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $21$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 7 \)
Character orbit:	\([\chi]\)	\(=\)	27.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(21\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	21	8	13
Cusp forms	15	8	7
Eisenstein series	6	0	6

Trace form

\( 8 q - 190 q^{4} - 884 q^{7} + O(q^{10}) \)

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.b.a	$27$	$7$	27.b	3.b	$2$	$2$	$2$	$6.211$	\(\Q(\sqrt{-10}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-806\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-26q^{4}+14\beta q^{5}-403q^{7}+\cdots\)
27.7.b.b	$27$	$7$	27.b	3.b	$2$	$2$	$2$	$6.211$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(598\)	$2\cdot 3$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+28q^{4}-40iq^{5}+299q^{7}+\cdots\)
27.7.b.c	$27$	$7$	27.b	3.b	$2$	$4$	$4$	$6.211$	\(\Q(i, \sqrt{41})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-676\)	$3^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{2}+(-7^{2}+\beta _{3})q^{4}+(7\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

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

\( S_{7}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{7}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{7}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)