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

• Label: 63.2.f
• Level: $63$
• Weight: $2$
• Character orbit: 63.f
• Rep. character: $\chi_{63}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $16$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(16\)
Trace bound:			\(2\)
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	12	8
Cusp forms	12	12	0
Eisenstein series	8	0	8

Trace form

12 * q - 2 * q^2 - 4 * q^3 - 6 * q^4 + 2 * q^5 - 8 * q^6 - 4 * q^9 - 4 * q^11 + 16 * q^12 - 4 * q^14 + 2 * q^15 - 6 * q^16 - 12 * q^17 + 22 * q^18 - 12 * q^19 + 22 * q^20 - 2 * q^21 + 6 * q^22 - 12 * q^23 - 12 * q^24 - 8 * q^26 + 20 * q^27 - 10 * q^29 - 8 * q^30 + 6 * q^31 + 8 * q^32 + 8 * q^33 - 6 * q^34 + 16 * q^35 - 38 * q^36 - 12 * q^37 - 14 * q^38 - 16 * q^39 - 12 * q^40 + 22 * q^41 + 20 * q^42 + 6 * q^43 + 76 * q^44 + 14 * q^45 + 24 * q^46 + 6 * q^47 - 14 * q^48 - 6 * q^49 - 4 * q^50 + 18 * q^51 + 18 * q^52 - 24 * q^53 - 44 * q^54 - 12 * q^55 - 12 * q^56 + 2 * q^57 + 18 * q^58 + 12 * q^59 - 20 * q^60 - 96 * q^62 - 8 * q^63 - 10 * q^65 + 34 * q^66 + 12 * q^67 - 12 * q^68 - 48 * q^69 + 36 * q^71 - 60 * q^72 - 36 * q^73 + 24 * q^74 + 22 * q^75 + 6 * q^76 - 8 * q^77 + 64 * q^78 + 6 * q^79 - 8 * q^80 + 32 * q^81 + 30 * q^83 + 2 * q^84 - 18 * q^85 - 40 * q^86 + 8 * q^87 - 6 * q^88 + 20 * q^89 + 100 * q^90 - 12 * q^91 - 18 * q^92 + 6 * q^93 - 6 * q^94 - 4 * q^95 + 32 * q^96 + 4 * q^98 - 28 * 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.f.a	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	\(\Q(\zeta_{18})\)	None		✓			63.2.f.a	$2$	$0$	\(-3\)	\(0\)	\(-3\)	\(-3\)	$3$	$\mathrm{SU}(2)[C_{3}]$	\(q+(\beta_{5}+\beta_1-1)q^{2}+(\beta_{5}-\beta_{3})q^{3}+\cdots\)
63.2.f.b	$63$	$2$	63.f	9.c	$3$	$6$	$3$	$0.503$	6.0.309123.1	None		✓			63.2.f.b	$2$	$0$	\(1\)	\(-4\)	\(5\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{2}-\beta _{3}+\beta _{5})q^{2}+(\beta _{2}+\beta _{3}+\cdots)q^{3}+\cdots\)