Space of modular forms of level 27, weight 5, and Character 27.b

• Label: 27.5.b
• Level: $27$
• Weight: $5$
• Character orbit: 27.b
• Rep. character: $\chi_{27}(26,\cdot)$
• Character field: $\Q$
• Dimension: $5$
• Newform subspaces: $3$
• Sturm bound: $15$
• Trace bound: $4$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 5 \)
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:			\(15\)
Trace bound:			\(4\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(27, [\chi])\).

	Total	New	Old
Modular forms	15	5	10
Cusp forms	9	5	4
Eisenstein series	6	0	6

Trace form

\( 5 q - 46 q^{4} + 67 q^{7} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(27, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.5.b.a	$27$	$5$	27.b	3.b	$2$	$1$	$1$	$2.791$	\(\Q\)	\(\Q(\sqrt{-3}) \)	✓	$2$	$0$	\(0\)	\(0\)	\(0\)	\(71\)	$1$	$\mathrm{U}(1)[D_{2}]$	\(q+2^{4}q^{4}+71q^{7}-337q^{13}+2^{8}q^{16}+\cdots\)
27.5.b.b	$27$	$5$	27.b	3.b	$2$	$2$	$2$	$2.791$	\(\Q(\sqrt{-6}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(34\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta q^{2}-38q^{4}+2\beta q^{5}+17q^{7}-22\beta q^{8}+\cdots\)
27.5.b.c	$27$	$5$	27.b	3.b	$2$	$2$	$2$	$2.791$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-38\)	$3$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{2}+7q^{4}+11iq^{5}-19q^{7}+23iq^{8}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(27, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)