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

• Label: 63.2.i
• Level: $63$
• Weight: $2$
• Character orbit: 63.i
• Rep. character: $\chi_{63}(5,\cdot)$
• Character field: $\Q(\zeta_{6})$
• 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.i (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
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 - 3 * q^3 - 10 * q^4 - 3 * q^5 + 6 * q^6 - 2 * q^7 - 3 * q^9 - 6 * q^10 - 9 * q^11 - 12 * q^12 - 3 * q^13 + 18 * q^14 + 6 * q^15 + 2 * q^16 + 9 * q^17 + 24 * q^18 - 6 * q^19 + 6 * q^20 - 3 * q^21 + 2 * q^22 - 6 * q^23 - 6 * q^24 + 3 * q^25 - 6 * q^26 - 27 * q^27 - 2 * q^28 - 24 * q^29 + 15 * q^30 - 3 * q^33 + 6 * q^34 - 12 * q^36 - q^37 + 27 * q^38 + 15 * q^39 + 24 * q^40 + 6 * q^41 - 24 * q^42 + 2 * q^43 - 27 * q^44 + 39 * q^45 - 4 * q^46 + 30 * q^47 + 15 * q^48 + 6 * q^49 - 9 * q^50 + 30 * q^51 - 15 * q^52 + 24 * q^53 + 27 * q^54 - 24 * q^56 - 27 * q^57 - q^58 - 36 * q^59 - 57 * q^60 - 24 * q^62 - 27 * q^63 + 4 * q^64 - 48 * q^66 + 12 * q^67 - 24 * q^68 + 12 * q^69 + 15 * q^70 - 30 * q^72 - 6 * q^73 - 51 * q^74 - 6 * q^75 + 48 * q^77 + 15 * q^78 - 24 * q^79 + 45 * q^80 + 33 * q^81 + 30 * q^83 + 87 * q^84 + 9 * q^85 + 57 * q^86 - 3 * q^87 - 11 * q^88 - 27 * q^89 - 51 * q^90 - 15 * q^91 + 30 * q^92 + 24 * q^93 + 51 * q^96 - 3 * q^97 - 21 * q^98 + 12 * 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.i.a	$63$	$2$	63.i	63.i	$6$	$2$	$1$	$0.503$	\(\Q(\sqrt{-3}) \)	None		✓			63.2.i.a	$2$	$0$	\(0\)	\(0\)	\(-3\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(1-2\zeta_{6})q^{2}+(1-2\zeta_{6})q^{3}-q^{4}+\cdots\)
63.2.i.b	$63$	$2$	63.i	63.i	$6$	$10$	$5$	$0.503$	10.0.\(\cdots\).1	None		✓	✓		63.2.i.b	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(-6\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-\beta _{3}-\beta _{5})q^{2}+(\beta _{1}-\beta _{7})q^{3}+(-1+\cdots)q^{4}+\cdots\)