Space of modular forms of level 63, weight 8, and Character 63.f

• Label: 63.8.f
• Level: $63$
• Weight: $8$
• Character orbit: 63.f
• Rep. character: $\chi_{63}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $84$
• Newform subspaces: $2$
• Sturm bound: $64$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
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:			\(64\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(63, [\chi])\).

	Total	New	Old
Modular forms	116	84	32
Cusp forms	108	84	24
Eisenstein series	8	0	8

Trace form

84 * q + 16 * q^2 - 52 * q^3 - 2688 * q^4 - 142 * q^5 + 862 * q^6 - 11340 * q^8 - 2344 * q^9 + 13964 * q^11 - 20708 * q^12 + 10976 * q^14 - 14710 * q^15 - 172032 * q^16 + 71916 * q^17 - 34214 * q^18 - 4188 * q^19 + 50854 * q^20 + 28126 * q^21 + 70512 * q^22 + 57444 * q^23 + 70530 * q^24 - 728244 * q^25 - 544760 * q^26 - 641500 * q^27 + 494990 * q^29 + 1469560 * q^30 + 198654 * q^31 + 894266 * q^32 - 314476 * q^33 + 212988 * q^34 - 686000 * q^35 - 2467424 * q^36 - 303564 * q^37 + 3077788 * q^38 + 1439072 * q^39 - 799500 * q^40 + 1099930 * q^41 + 1159340 * q^42 - 720642 * q^43 - 8659904 * q^44 - 1440922 * q^45 + 2164488 * q^46 - 198498 * q^47 + 10341268 * q^48 - 4941258 * q^49 + 1226570 * q^50 - 2634678 * q^51 - 2243574 * q^52 - 9872952 * q^53 - 2037950 * q^54 + 2699268 * q^55 + 2107392 * q^56 + 6978014 * q^57 + 2589534 * q^58 - 412116 * q^59 + 13736092 * q^60 - 10152312 * q^62 - 496664 * q^63 + 6681204 * q^64 + 202310 * q^65 - 1918034 * q^66 - 5109396 * q^67 - 19893666 * q^68 - 2713152 * q^69 - 7015212 * q^71 - 1935510 * q^72 + 9608292 * q^73 + 6731988 * q^74 + 1459870 * q^75 + 7703844 * q^76 + 3652264 * q^77 + 14231212 * q^78 - 2735922 * q^79 + 73364824 * q^80 + 35255372 * q^81 - 18805500 * q^82 - 11773050 * q^83 - 22674358 * q^84 + 1923246 * q^85 - 31205326 * q^86 - 47889304 * q^87 + 28789032 * q^88 + 86767220 * q^89 + 2088784 * q^90 - 8474844 * q^91 - 41269086 * q^92 - 24770802 * q^93 - 13619922 * q^94 + 17309660 * q^95 - 90426088 * q^96 - 13339620 * q^97 - 3764768 * q^98 + 50692292 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(63, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
63.8.f.a	$63$	$8$	63.f	9.c	$3$	$42$	$21$	$19.680$		None		✓			63.8.f.a	$2$	$0$	\(-8\)	\(56\)	\(-571\)	\(7203\)		$\mathrm{SU}(2)[C_{3}]$
63.8.f.b	$63$	$8$	63.f	9.c	$3$	$42$	$21$	$19.680$		None		✓			63.8.f.b	$2$	$0$	\(24\)	\(-108\)	\(429\)	\(-7203\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{8}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)