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

• Label: 63.10.f
• Level: $63$
• Weight: $10$
• Character orbit: 63.f
• Rep. character: $\chi_{63}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $108$
• Newform subspaces: $2$
• Sturm bound: $80$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	63.f (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(80\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	148	108	40
Cusp forms	140	108	32
Eisenstein series	8	0	8

Trace form

108 * q - 32 * q^2 + 2 * q^3 - 13824 * q^4 + 1592 * q^5 + 5230 * q^6 + 30996 * q^8 + 63434 * q^9 - 182890 * q^11 + 578140 * q^12 - 153664 * q^14 - 860236 * q^15 - 3538944 * q^16 - 726636 * q^17 + 2538538 * q^18 + 787860 * q^19 - 742778 * q^20 - 19208 * q^21 - 1056672 * q^22 - 1835472 * q^23 - 3719598 * q^24 - 19632294 * q^25 - 8489528 * q^26 + 14560400 * q^27 - 7665028 * q^29 - 34246760 * q^30 - 3089124 * q^31 - 18163318 * q^32 + 42239594 * q^33 - 1964628 * q^34 + 24010000 * q^35 - 15831200 * q^36 - 19829232 * q^37 - 28235060 * q^38 - 81515920 * q^39 + 29092500 * q^40 - 26548418 * q^41 + 30300620 * q^42 + 1570806 * q^43 + 556002112 * q^44 + 159486572 * q^45 + 20937096 * q^46 - 176311308 * q^47 - 382520348 * q^48 - 311299254 * q^49 - 351636550 * q^50 + 10625826 * q^51 + 107023194 * q^52 + 477368400 * q^53 + 499466818 * q^54 - 53761752 * q^55 - 118013952 * q^56 - 629935798 * q^57 - 213788322 * q^58 - 300412986 * q^59 - 27996692 * q^60 + 292253736 * q^62 + 167695444 * q^63 + 2687275764 * q^64 - 684093976 * q^65 - 2362534562 * q^66 - 307154646 * q^67 - 441460002 * q^68 + 96454560 * q^69 + 1229506272 * q^71 + 1811814570 * q^72 - 507026628 * q^73 - 1965773532 * q^74 - 2693658914 * q^75 - 469171548 * q^76 - 281224328 * q^77 + 621372028 * q^78 + 204676524 * q^79 + 2668342744 * q^80 + 786102866 * q^81 + 404754084 * q^82 - 2548632732 * q^83 + 738341114 * q^84 + 241472016 * q^85 - 595283614 * q^86 - 937487044 * q^87 - 2090012760 * q^88 - 824660800 * q^89 - 3829176752 * q^90 + 859346712 * q^91 + 621087426 * q^92 + 1864118532 * q^93 + 3150940446 * q^94 - 3491703700 * q^95 + 7392160376 * q^96 + 986710410 * q^97 + 368947264 * q^98 - 649818568 * 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.f.a	$63$	$10$	63.f	9.c	$3$	$54$	$27$	$32.447$		None		✓			63.10.f.a	$2$	$0$	\(-48\)	\(9\)	\(-1704\)	\(-64827\)		$\mathrm{SU}(2)[C_{3}]$
63.10.f.b	$63$	$10$	63.f	9.c	$3$	$54$	$27$	$32.447$		None		✓			63.10.f.b	$2$	$0$	\(16\)	\(-7\)	\(3296\)	\(64827\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{10}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{10}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)