Space of modular forms of level 27, weight 4, and Character 27.c

• Label: 27.4.c
• Level: $27$
• Weight: $4$
• Character orbit: 27.c
• Rep. character: $\chi_{27}(10,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.c (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(27, [\chi])\).

	Total	New	Old
Modular forms	24	8	16
Cusp forms	12	4	8
Eisenstein series	12	4	8

Trace form

\( 4 q + 3 q^{2} - 5 q^{4} + 15 q^{5} - 7 q^{7} - 66 q^{8} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(27, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
27.4.c.a	$27$	$4$	27.c	9.c	$3$	$4$	$2$	$1.593$	\(\Q(\sqrt{-3}, \sqrt{-11})\)	None			✓	✓	9.4.c.a	$2$	$0$	\(3\)	\(0\)	\(15\)	\(-7\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta _{1}+\beta _{3})q^{2}+(-4+\beta _{1}-3\beta _{2}+3\beta _{3})q^{4}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(27, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(27, [\chi]) \simeq \) \(S_{4}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)