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

• Label: 63.6.i
• Level: $63$
• Weight: $6$
• Character orbit: 63.i
• Rep. character: $\chi_{63}(5,\cdot)$
• 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.i (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^3 - 1154 * q^4 - 3 * q^5 + 96 * q^6 - 30 * q^7 + 489 * q^9 - 6 * q^10 + 567 * q^11 - 1542 * q^12 + 543 * q^13 - 1638 * q^14 + 234 * q^15 + 16446 * q^16 - 801 * q^17 - 2022 * q^18 - 6 * q^19 + 96 * q^20 - 4119 * q^21 + 62 * q^22 + 7806 * q^23 - 2346 * q^24 - 18749 * q^25 + 10128 * q^26 - 1539 * q^27 + 860 * q^28 + 17904 * q^29 + 11457 * q^30 - 3 * q^33 + 96 * q^34 + 3960 * q^35 - 57846 * q^36 + 2577 * q^37 + 14967 * q^38 - 16269 * q^39 + 9564 * q^40 + 28230 * q^41 + 15606 * q^42 - 9246 * q^43 - 69885 * q^44 - 23649 * q^45 - 9418 * q^46 - 56562 * q^47 + 48615 * q^48 + 7948 * q^49 - 67509 * q^50 - 103722 * q^51 - 40899 * q^52 + 25296 * q^53 + 176211 * q^54 + 104754 * q^56 + 33399 * q^57 - 4951 * q^58 - 59076 * q^59 + 33729 * q^60 + 79536 * q^62 - 95871 * q^63 - 198600 * q^64 + 114900 * q^66 + 1244 * q^67 + 191496 * q^68 + 3702 * q^69 - 127197 * q^70 + 183582 * q^72 - 6 * q^73 - 45681 * q^74 - 240486 * q^75 - 2880 * q^76 + 13854 * q^77 + 184431 * q^78 + 59984 * q^79 + 243225 * q^80 + 177117 * q^81 + 90 * q^82 - 246930 * q^83 + 56085 * q^84 + 11973 * q^85 + 291801 * q^86 + 205125 * q^87 - 34751 * q^88 - 6345 * q^89 - 269187 * q^90 - 120111 * q^91 - 463488 * q^92 + 200946 * q^93 - 382521 * 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.i.a	$63$	$6$	63.i	63.i	$6$	$76$	$38$	$10.104$		None		✓	✓	✓	63.6.i.a	$2$	$0$	\(0\)	\(-3\)	\(-3\)	\(-30\)		$\mathrm{SU}(2)[C_{6}]$