Space of modular forms of level 63, weight 2, and Character 63.o

• Label: 63.2.o
• Level: $63$
• Weight: $2$
• Character orbit: 63.o
• Rep. character: $\chi_{63}(20,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $1$
• Sturm bound: $16$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(16\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(63, [\chi])\).

	Total	New	Old
Modular forms	20	20	0
Cusp forms	12	12	0
Eisenstein series	8	8	0

Trace form

12 * q - 6 * q^2 + 2 * q^4 - 2 * q^7 - 12 * q^9 - 12 * q^14 + 6 * q^15 + 2 * q^16 - 6 * q^18 - 24 * q^21 - 10 * q^22 + 24 * q^23 - 8 * q^28 + 30 * q^29 + 48 * q^30 - 12 * q^32 + 18 * q^36 - 4 * q^37 + 36 * q^42 - 10 * q^43 - 40 * q^46 + 6 * q^49 - 36 * q^50 - 42 * q^51 + 42 * q^56 - 18 * q^57 + 2 * q^58 - 12 * q^60 + 24 * q^63 + 16 * q^64 - 78 * q^65 + 12 * q^67 + 18 * q^70 - 24 * q^72 - 12 * q^74 - 24 * q^77 - 12 * q^78 - 6 * q^79 + 24 * q^81 - 60 * q^84 - 6 * q^85 + 96 * q^86 + 34 * q^88 - 24 * q^91 + 30 * q^92 + 78 * q^93 + 72 * q^95 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.2.o.a	$63$	$2$	63.o	63.o	$6$	$12$	$6$	$0.503$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓	✓	63.2.o.a	$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-2\)	$3$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{1}q^{2}-\beta _{2}q^{3}+(\beta _{1}+\beta _{4}+\beta _{7})q^{4}+\cdots\)