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

• Label: 63.6.f
• Level: $63$
• Weight: $6$
• Character orbit: 63.f
• Rep. character: $\chi_{63}(22,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $60$
• Newform subspaces: $2$
• Sturm bound: $48$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(48\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(63, [\chi])\).

	Total	New	Old
Modular forms	84	60	24
Cusp forms	76	60	16
Eisenstein series	8	0	8

Trace form

60 * q - 8 * q^2 + 20 * q^3 - 480 * q^4 - 58 * q^5 - 122 * q^6 + 1620 * q^8 + 224 * q^9 - 700 * q^11 - 3812 * q^12 - 784 * q^14 + 4634 * q^15 - 7680 * q^16 + 3012 * q^17 + 12106 * q^18 - 1788 * q^19 - 4538 * q^20 + 490 * q^21 - 1896 * q^22 - 14988 * q^23 + 7218 * q^24 - 15444 * q^25 + 20296 * q^26 + 16292 * q^27 - 10678 * q^29 - 19400 * q^30 - 4434 * q^31 - 25558 * q^32 + 35156 * q^33 - 20316 * q^34 + 19600 * q^35 + 19456 * q^36 + 20028 * q^37 + 29572 * q^38 + 17264 * q^39 + 9300 * q^40 - 15074 * q^41 - 40180 * q^42 - 6306 * q^43 - 82688 * q^44 - 62398 * q^45 - 53880 * q^46 + 63150 * q^47 + 103684 * q^48 - 72030 * q^49 + 65330 * q^50 + 4506 * q^51 + 45882 * q^52 + 120504 * q^53 - 68390 * q^54 + 27588 * q^55 - 37632 * q^56 + 180074 * q^57 - 6498 * q^58 + 59700 * q^59 - 298292 * q^60 - 249144 * q^62 - 9800 * q^63 + 242676 * q^64 - 886 * q^65 - 160322 * q^66 + 15540 * q^67 + 295998 * q^68 + 18288 * q^69 + 206100 * q^71 - 92118 * q^72 - 160884 * q^73 + 6900 * q^74 + 54526 * q^75 + 93252 * q^76 - 47432 * q^77 - 464948 * q^78 + 36030 * q^79 - 524456 * q^80 - 38356 * q^81 + 467316 * q^82 - 93570 * q^83 - 22246 * q^84 - 72774 * q^85 + 81674 * q^86 + 547016 * q^87 - 270552 * q^88 + 470540 * q^89 + 937888 * q^90 + 32340 * q^91 - 278334 * q^92 - 634230 * q^93 - 242562 * q^94 - 444340 * q^95 - 339976 * q^96 + 1404 * q^97 + 38416 * q^98 - 101548 * 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.f.a	$63$	$6$	63.f	9.c	$3$	$30$	$15$	$10.104$		None		✓			63.6.f.a	$2$	$0$	\(-12\)	\(0\)	\(-129\)	\(-735\)		$\mathrm{SU}(2)[C_{3}]$
63.6.f.b	$63$	$6$	63.f	9.c	$3$	$30$	$15$	$10.104$		None		✓			63.6.f.b	$2$	$0$	\(4\)	\(20\)	\(71\)	\(735\)		$\mathrm{SU}(2)[C_{3}]$

Decomposition of \(S_{6}^{\mathrm{old}}(63, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{6}^{\mathrm{new}}(9, [\chi])\)\(^{\oplus 2}\)