Space of modular forms of level 64, weight 9, and Character 64.j

• Label: 64.9.j
• Level: $64$
• Weight: $9$
• Character orbit: 64.j
• Rep. character: $\chi_{64}(3,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $504$
• Newform subspaces: $1$
• Sturm bound: $72$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 64 = 2^{6} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	64.j (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 64 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(72\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{9}(64, [\chi])\).

	Total	New	Old
Modular forms	520	520	0
Cusp forms	504	504	0
Eisenstein series	16	16	0

Trace form

504 * q - 8 * q^2 - 8 * q^3 - 8 * q^4 - 8 * q^5 - 8 * q^6 - 8 * q^7 - 8 * q^8 - 8 * q^9 - 8 * q^10 - 8 * q^11 - 8 * q^12 - 8 * q^13 - 8 * q^14 - 8 * q^15 - 8 * q^16 - 8 * q^17 - 8 * q^18 - 8 * q^19 - 8 * q^20 - 8 * q^21 - 1068272 * q^22 - 8 * q^23 + 322272 * q^24 - 8 * q^25 - 3364208 * q^26 - 8 * q^27 + 3615232 * q^28 - 8 * q^29 + 7934312 * q^30 - 16 * q^31 - 4840928 * q^32 - 8276528 * q^34 - 8 * q^35 + 7200392 * q^36 - 8 * q^37 + 16322032 * q^38 - 8 * q^39 - 1151648 * q^40 - 8 * q^41 - 35148528 * q^42 - 8 * q^43 + 22652128 * q^44 - 8 * q^45 - 8 * q^46 - 8 * q^47 - 8 * q^48 - 8 * q^49 - 5145200 * q^50 + 55448056 * q^51 - 45948152 * q^52 - 8 * q^53 + 79361848 * q^54 - 92653576 * q^55 + 56874880 * q^56 - 8 * q^57 - 50876288 * q^58 + 89877496 * q^59 - 163708136 * q^60 - 8 * q^61 - 43933720 * q^62 + 96767896 * q^64 - 16 * q^65 + 227317848 * q^66 - 186760968 * q^67 + 81864712 * q^68 - 8 * q^69 - 92889896 * q^70 + 159664120 * q^71 - 261232784 * q^72 - 8 * q^73 - 170028944 * q^74 + 51674104 * q^75 + 159303864 * q^76 - 8 * q^77 + 68388208 * q^78 - 144406536 * q^79 + 332920480 * q^80 - 8 * q^81 + 69799592 * q^82 - 8 * q^83 - 689231320 * q^84 - 8 * q^85 - 554580944 * q^86 - 8 * q^87 + 45587912 * q^88 - 8 * q^89 + 873269992 * q^90 - 8 * q^91 + 1093020592 * q^92 - 52496 * q^93 + 310515736 * q^94 - 16 * q^95 - 468840832 * q^96 - 1202501264 * q^98 + 52480 * q^99

Decomposition of \(S_{9}^{\mathrm{new}}(64, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
64.9.j.a	$64$	$9$	64.j	64.j	$16$	$504$	$63$	$26.072$		None		✓	✓	✓	64.9.j.a	$2$	$0$	\(-8\)	\(-8\)	\(-8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$