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

• Label: 63.6.h
• Level: $63$
• Weight: $6$
• Character orbit: 63.h
• Rep. character: $\chi_{63}(25,\cdot)$
• Character field: $\Q(\zeta_{3})$
• 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.h (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
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 - 2 * q^2 - q^3 + 1150 * q^4 + 101 * q^5 - 116 * q^6 + 28 * q^7 - 72 * q^8 - 271 * q^9 - 66 * q^10 + 191 * q^11 - 1550 * q^12 + 179 * q^13 + 416 * q^14 - 1828 * q^15 + 16318 * q^16 + 2043 * q^17 + 1732 * q^18 - 64 * q^19 + 2782 * q^20 + 847 * q^21 - 66 * q^22 + 2604 * q^23 - 10746 * q^24 - 18749 * q^25 + 4798 * q^26 - 5551 * q^27 + 796 * q^28 - 4552 * q^29 + 9661 * q^30 - 2170 * q^31 - 1306 * q^32 - 6979 * q^33 + 30 * q^34 - 24356 * q^35 + 3730 * q^36 - 2581 * q^37 + 22255 * q^38 + 1919 * q^39 + 1014 * q^40 + 46630 * q^41 + 49964 * q^42 + 9242 * q^43 + 19261 * q^44 + 59897 * q^45 + 9414 * q^46 - 69510 * q^47 - 111629 * q^48 + 4288 * q^49 - 78097 * q^50 + 8358 * q^51 + 9473 * q^52 + 31848 * q^53 - 111779 * q^54 + 22314 * q^55 - 33336 * q^56 + 65525 * q^57 - 5079 * q^58 - 186780 * q^59 - 138659 * q^60 + 96284 * q^61 - 301716 * q^62 - 136187 * q^63 + 194488 * q^64 - 15292 * q^65 - 84614 * q^66 + 1244 * q^67 + 138522 * q^68 + 253152 * q^69 - 60033 * q^70 - 13062 * q^71 + 214518 * q^72 - 42016 * q^73 + 82035 * q^74 + 122134 * q^75 - 3010 * q^76 + 20356 * q^77 - 172115 * q^78 + 25088 * q^79 + 190471 * q^80 + 263045 * q^81 + 30 * q^82 + 177090 * q^83 + 619115 * q^84 - 5727 * q^85 - 17335 * q^86 + 235181 * q^87 + 30657 * q^88 + 176927 * q^89 - 238307 * q^90 - 21451 * q^91 - 112980 * q^92 - 138120 * q^93 - 192738 * q^94 - 198694 * q^95 + 971 * q^96 - 34681 * q^97 - 282479 * q^98 + 54410 * 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.h.a	$63$	$6$	63.h	63.h	$3$	$76$	$38$	$10.104$		None		✓	✓	✓	63.6.g.a	$2$	$0$	\(-2\)	\(-1\)	\(101\)	\(28\)		$\mathrm{SU}(2)[C_{3}]$