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

• Label: 63.9.b
• Level: $63$
• Weight: $9$
• Character orbit: 63.b
• Rep. character: $\chi_{63}(8,\cdot)$
• Character field: $\Q$
• Dimension: $16$
• 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.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 3 \)
Character field:			\(\Q\)
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	68	16	52
Cusp forms	60	16	44
Eisenstein series	8	0	8

Trace form

\( 16 q - 3000 q^{4} + O(q^{10}) \)

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.b.a	$63$	$9$	63.b	3.b	$2$	$16$	$16$	$25.665$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{15}\cdot 3^{33}\cdot 7^{14}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{8}q^{2}+(-187-\beta _{1})q^{4}+(\beta _{8}+\beta _{10}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{9}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{9}^{\mathrm{old}}(63, [\chi]) \cong \) \(S_{9}^{\mathrm{new}}(3, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{9}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)