Space of modular forms of level 63, weight 3, and Character 63.k

• Label: 63.3.k
• Level: $63$
• Weight: $3$
• Character orbit: 63.k
• Rep. character: $\chi_{63}(31,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $28$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	63.k (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(63, [\chi])\).

	Total	New	Old
Modular forms	36	36	0
Cusp forms	28	28	0
Eisenstein series	8	8	0

Trace form

\( 28 q + q^{2} - 3 q^{3} - 23 q^{4} + 12 q^{6} - 16 q^{8} + 9 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.3.k.a	$63$	$3$	63.k	63.k	$6$	$28$	$14$	$1.717$		None		✓	✓	✓	63.3.k.a	$2$	$0$	\(1\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$