Space of modular forms of level 5, weight 9, and Character 5.c

• Label: 5.9.c
• Level: $5$
• Weight: $9$
• Character orbit: 5.c
• Rep. character: $\chi_{5}(2,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $4$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 9 \)
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:			\(4\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(5, [\chi])\).

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

Trace form

\( 6 q - 2 q^{2} - 72 q^{3} + 220 q^{5} + 1752 q^{6} - 2352 q^{7} - 8220 q^{8} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(5, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
5.9.c.a	$5$	$9$	5.c	5.c	$4$	$6$	$3$	$2.037$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None		$2$	$0$	\(-2\)	\(-72\)	\(220\)	\(-2352\)	$2^{6}\cdot 5^{2}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{3}q^{2}+(-12-12\beta _{1}-\beta _{2}-\beta _{5})q^{3}+\cdots\)