Space of modular forms of level 63, weight 9, and Character 63.t

• Label: 63.9.t
• Level: $63$
• Weight: $9$
• Character orbit: 63.t
• Rep. character: $\chi_{63}(40,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $124$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	63.t (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(63, [\chi])\).

	Total	New	Old
Modular forms	132	132	0
Cusp forms	124	124	0
Eisenstein series	8	8	0

Trace form

\( 124 q - 2 q^{2} - 3 q^{3} + 15358 q^{4} - 3 q^{5} - 768 q^{6} - 924 q^{7} - 520 q^{8} - 9375 q^{9} + O(q^{10}) \)

Decomposition of \(S_{9}^{\mathrm{new}}(63, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.9.t.a	$63$	$9$	63.t	63.t	$6$	$124$	$62$	$25.665$		None		$2$	$0$	\(-2\)	\(-3\)	\(-3\)	\(-924\)		$\mathrm{SU}(2)[C_{6}]$