Space of modular forms of level 63, weight 6, and Character 63.s

• Label: 63.6.s
• Level: $63$
• Weight: $6$
• Character orbit: 63.s
• Rep. character: $\chi_{63}(47,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	63.s (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(63, [\chi])\).

	Total	New	Old
Modular forms	84	84	0
Cusp forms	76	76	0
Eisenstein series	8	8	0

Trace form

76 * q - 3 * q^2 - 3 * q^3 + 577 * q^4 - 6 * q^5 - 96 * q^6 - 30 * q^7 - 81 * q^9 - 6 * q^10 - 3 * q^12 - 543 * q^13 - 123 * q^14 + 234 * q^15 - 8223 * q^16 + 801 * q^17 + 5721 * q^18 - 6 * q^19 - 96 * q^20 + 300 * q^21 + 62 * q^22 - 5034 * q^24 + 37498 * q^25 - 10128 * q^26 + 1539 * q^27 + 860 * q^28 + 17904 * q^29 - 20112 * q^30 + 3249 * q^31 + 10299 * q^32 - 28680 * q^33 - 96 * q^34 - 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 29934 * q^38 + 16422 * q^39 - 28230 * q^41 + 3369 * q^42 - 9246 * q^43 + 69885 * q^44 - 29532 * q^45 - 9418 * q^46 - 28281 * q^47 - 48615 * q^48 + 2458 * q^49 - 67509 * q^50 + 68088 * q^51 - 25296 * q^53 + 237600 * q^54 + 27288 * q^56 + 33399 * q^57 + 9902 * q^58 - 29538 * q^59 - 64884 * q^60 + 4206 * q^61 - 79536 * q^62 - 141630 * q^63 - 198600 * q^64 - 173388 * q^65 + 119325 * q^66 - 622 * q^67 + 382992 * q^68 - 3702 * q^69 + 14178 * q^70 + 135561 * q^72 - 6 * q^73 + 48207 * q^75 + 2880 * q^76 - 238866 * q^77 + 184431 * q^78 - 29992 * q^79 - 243225 * q^80 + 61827 * q^81 + 90 * q^82 + 246930 * q^83 - 108525 * q^84 + 11973 * q^85 - 9933 * q^87 + 69502 * q^88 + 6345 * q^89 + 269187 * q^90 - 120111 * q^91 - 463488 * q^92 - 341118 * q^93 - 3 * q^94 - 267813 * q^95 - 572118 * q^96 + 104037 * q^97 + 646797 * q^98 - 144540 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.6.s.a	$63$	$6$	63.s	63.s	$6$	$76$	$38$	$10.104$		None		✓	✓	✓	63.6.i.a	$2$	$0$	\(-3\)	\(-3\)	\(-6\)	\(-30\)		$\mathrm{SU}(2)[C_{6}]$