Space of modular forms of level 63, weight 10, and Character 63.g

• Label: 63.10.g
• Level: $63$
• Weight: $10$
• Character orbit: 63.g
• Rep. character: $\chi_{63}(4,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $140$
• Newform subspaces: $1$
• Sturm bound: $80$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	63.g (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(80\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(63, [\chi])\).

	Total	New	Old
Modular forms	148	148	0
Cusp forms	140	140	0
Eisenstein series	8	8	0

Trace form

140 * q + q^2 - q^3 - 17407 * q^4 - 5002 * q^5 - 5060 * q^6 - 343 * q^7 - 1032 * q^8 - 16051 * q^9 - 1026 * q^10 - 30826 * q^11 + 95719 * q^12 - 32438 * q^13 - 288115 * q^14 + 347087 * q^15 - 4193791 * q^16 + 405054 * q^17 + 1574293 * q^18 - 223382 * q^19 + 1396222 * q^20 + 246370 * q^21 - 1026 * q^22 + 4511418 * q^23 + 5274774 * q^24 + 48437498 * q^25 + 7321342 * q^26 + 4933928 * q^27 - 612868 * q^28 - 1558012 * q^29 - 17070620 * q^30 + 3904381 * q^31 + 15521453 * q^32 - 1247377 * q^33 + 510 * q^34 + 5841649 * q^35 + 37393330 * q^36 + 3238450 * q^37 - 24316478 * q^38 + 6443435 * q^39 - 2855628 * q^40 + 26345152 * q^41 + 40536359 * q^42 - 16035014 * q^43 - 4368035 * q^44 - 54795103 * q^45 + 6427998 * q^46 + 78250539 * q^47 - 171302045 * q^48 - 66445453 * q^49 + 170200463 * q^50 - 56039535 * q^51 + 67479550 * q^52 - 129259542 * q^53 + 103008178 * q^54 + 34460634 * q^55 - 450674574 * q^56 - 62534386 * q^57 - 102971202 * q^58 + 278657415 * q^59 - 150163628 * q^60 - 69192125 * q^61 + 59045916 * q^62 - 193328363 * q^63 + 1878522872 * q^64 + 225922931 * q^65 + 840587881 * q^66 + 139249279 * q^67 - 148527060 * q^68 + 516608445 * q^69 - 240989148 * q^70 + 946107420 * q^71 + 767160477 * q^72 - 345099890 * q^73 + 71246730 * q^74 - 711483752 * q^75 - 228480002 * q^76 + 215828035 * q^77 - 928742963 * q^78 - 439610579 * q^79 + 917631511 * q^80 + 313020569 * q^81 + 510 * q^82 + 1806647628 * q^83 - 628879129 * q^84 + 256968123 * q^85 - 737796466 * q^86 - 872106226 * q^87 - 267384834 * q^88 + 394034828 * q^89 - 117361547 * q^90 + 61002520 * q^91 - 2916571860 * q^92 - 357415299 * q^93 - 757693119 * q^94 + 952263707 * q^95 - 3619363564 * q^96 - 226043930 * q^97 - 5906269583 * q^98 - 2515013275 * q^99

Decomposition of \(S_{10}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.10.g.a	$63$	$10$	63.g	63.g	$3$	$140$	$70$	$32.447$		None		✓	✓	✓	63.10.g.a	$2$	$0$	\(1\)	\(-1\)	\(-5002\)	\(-343\)		$\mathrm{SU}(2)[C_{3}]$