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

• Label: 63.8.p
• Level: $63$
• Weight: $8$
• Character orbit: 63.p
• Rep. character: $\chi_{63}(17,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $36$
• Newform subspaces: $1$
• Sturm bound: $64$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 63 = 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	63.p (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 21 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(64\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	120	36	84
Cusp forms	104	36	68
Eisenstein series	16	0	16

Trace form

36 * q + 1024 * q^4 - 2074 * q^7 + 1248 * q^10 - 59708 * q^16 - 105330 * q^19 + 544 * q^22 - 56250 * q^25 + 556220 * q^28 + 86862 * q^31 + 591034 * q^37 - 3036324 * q^40 - 837332 * q^43 + 3896752 * q^46 + 6626454 * q^49 - 11085900 * q^52 - 134084 * q^58 + 4324644 * q^61 - 11555464 * q^64 + 8750706 * q^67 + 8823972 * q^70 - 744402 * q^73 + 1136238 * q^79 - 29281932 * q^82 + 18719472 * q^85 - 4365916 * q^88 + 21779742 * q^91 + 96093708 * q^94

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.p.a	$63$	$8$	63.p	21.g	$6$	$36$	$18$	$19.680$		None		✓	✓	✓	63.8.p.a	$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2074\)		$\mathrm{SU}(2)[C_{6}]$

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

\( S_{8}^{\mathrm{old}}(63, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(21, [\chi])\)\(^{\oplus 2}\)