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

• Label: 63.6.o
• Level: $63$
• Weight: $6$
• Character orbit: 63.o
• Rep. character: $\chi_{63}(20,\cdot)$
• Character field: $\Q(\zeta_{6})$
• 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.o (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 63 \)
Character field:			\(\Q(\zeta_{6})\)
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 - 6 * q^2 + 574 * q^4 - 30 * q^7 + 156 * q^9 - 576 * q^11 + 1392 * q^14 - 666 * q^15 - 8130 * q^16 + 3798 * q^18 + 4194 * q^21 - 130 * q^22 - 8112 * q^23 - 18752 * q^25 - 1732 * q^28 - 35826 * q^29 + 19104 * q^30 - 1092 * q^32 + 71190 * q^36 + 10308 * q^37 - 5016 * q^39 + 51450 * q^42 + 18486 * q^43 - 38056 * q^46 + 7948 * q^49 + 76104 * q^50 - 2346 * q^51 + 164652 * q^56 - 150102 * q^57 + 9902 * q^58 - 115356 * q^60 - 168468 * q^63 - 192648 * q^64 + 12666 * q^65 + 1244 * q^67 + 33024 * q^70 - 17364 * q^72 + 356496 * q^74 - 16458 * q^77 - 412764 * q^78 + 168074 * q^79 - 148872 * q^81 + 162282 * q^84 + 2598 * q^85 + 543300 * q^86 + 69694 * q^88 + 139368 * q^91 - 211794 * q^92 - 196818 * q^93 - 950328 * q^95 + 325080 * 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.o.a	$63$	$6$	63.o	63.o	$6$	$76$	$38$	$10.104$		None		✓	✓	✓	63.6.o.a	$4$	$0$	\(-6\)	\(0\)	\(0\)	\(-30\)		$\mathrm{SU}(2)[C_{6}]$