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

• Label: 5.27.c
• Level: $5$
• Weight: $27$
• Character orbit: 5.c
• Rep. character: $\chi_{5}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $1$
• Sturm bound: $13$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 27 \)
Character orbit:	\([\chi]\)	\(=\)	5.c (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(13\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	28	28	0
Cusp forms	24	24	0
Eisenstein series	4	4	0

Trace form

\( 24 q + 8190 q^{2} + 1867680 q^{3} - 140947920 q^{5} - 3382472712 q^{6} - 99234643200 q^{7} - 2004366809340 q^{8} + O(q^{10}) \)

Decomposition of \(S_{27}^{\mathrm{new}}(5, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.27.c.a	$5$	$27$	5.c	5.c	$4$	$24$	$12$	$21.415$		None		$2$	$0$	\(8190\)	\(1867680\)	\(-140947920\)	\(-99234643200\)		$\mathrm{SU}(2)[C_{4}]$