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

• Label: 63.2.g
• Level: $63$
• Weight: $2$
• Character orbit: 63.g
• Rep. character: $\chi_{63}(4,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $1$

Defining parameters

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

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 + q^2 - q^3 - 3 * q^4 - 10 * q^5 - 2 * q^6 - 12 * q^8 - q^9 - 6 * q^10 + 2 * q^11 + 19 * q^12 - 3 * q^13 + 11 * q^14 - 16 * q^15 + 3 * q^16 + 9 * q^17 + q^18 + 4 * q^20 - 8 * q^21 - 6 * q^22 + 12 * q^24 - 6 * q^25 + 16 * q^26 - 7 * q^27 - 6 * q^28 + 8 * q^29 - 26 * q^30 - 3 * q^31 - 7 * q^32 - 16 * q^33 + 4 * q^35 + 40 * q^36 - 3 * q^37 - 38 * q^38 + 20 * q^39 + 12 * q^40 + 10 * q^41 + 41 * q^42 - 6 * q^43 - 5 * q^44 - 4 * q^45 + 27 * q^47 - 5 * q^48 + 12 * q^49 + 23 * q^50 + 24 * q^51 + 30 * q^52 - 12 * q^53 - 62 * q^54 - 6 * q^55 - 48 * q^56 - q^57 + 18 * q^58 + 30 * q^59 - 38 * q^60 - 12 * q^62 - 20 * q^63 - 36 * q^64 - 16 * q^65 - 41 * q^66 - 6 * q^67 - 60 * q^68 + 6 * q^69 - 24 * q^70 - 30 * q^71 + 39 * q^72 + 12 * q^73 + 78 * q^74 + 43 * q^75 + 6 * q^76 - 26 * q^77 - 35 * q^78 - 12 * q^79 + 19 * q^80 - q^81 + 18 * q^83 + 5 * q^84 - 3 * q^85 + 14 * q^86 + 29 * q^87 + 6 * q^88 + 41 * q^89 + 25 * q^90 + 21 * q^91 + 30 * q^92 - 12 * q^93 - 3 * q^94 - 13 * q^95 + 14 * q^96 - 3 * q^97 + 61 * q^98 + 50 * 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.g.a	$63$	$2$	63.g	63.g	$3$	$2$	$1$	$0.503$	\(\Q(\sqrt{-3}) \)	None		✓			63.2.g.a	$2$	$0$	\(-1\)	\(-3\)	\(-2\)	\(1\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q-\zeta_{6}q^{2}+(-1-\zeta_{6})q^{3}+(1-\zeta_{6})q^{4}+\cdots\)
63.2.g.b	$63$	$2$	63.g	63.g	$3$	$10$	$5$	$0.503$	10.0.\(\cdots\).1	None		✓	✓		63.2.g.b	$2$	$0$	\(2\)	\(2\)	\(-8\)	\(-1\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+\beta _{1}q^{2}+(\beta _{2}-\beta _{7})q^{3}+(-1-\beta _{2}+\cdots)q^{4}+\cdots\)