Space of modular forms of level 32, weight 8, and Character 32.g

• Label: 32.8.g
• Level: $32$
• Weight: $8$
• Character orbit: 32.g
• Rep. character: $\chi_{32}(5,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $108$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.g (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 32 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(32\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{8}(32, [\chi])\).

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

Trace form

108 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 - 4 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^8 - 4 * q^9 - 13004 * q^10 - 4 * q^11 + 30668 * q^12 - 4 * q^13 - 26196 * q^14 - 52784 * q^16 + 102056 * q^18 - 4 * q^19 + 81996 * q^20 - 4 * q^21 - 374240 * q^22 - 143420 * q^23 + 380880 * q^24 - 4 * q^25 - 363984 * q^26 + 476084 * q^27 - 195464 * q^28 - 4 * q^29 + 870468 * q^30 - 714992 * q^31 + 535656 * q^32 - 8 * q^33 - 201072 * q^34 + 816500 * q^35 - 1669712 * q^36 - 4 * q^37 - 2533100 * q^38 - 283948 * q^39 + 2746344 * q^40 - 4 * q^41 + 4924936 * q^42 + 366180 * q^43 - 1585404 * q^44 + 8744 * q^45 - 2715812 * q^46 - 5044368 * q^48 - 1653804 * q^50 + 3002072 * q^51 + 8882212 * q^52 - 1815636 * q^53 + 6815776 * q^54 - 4191012 * q^55 - 3655000 * q^56 - 4 * q^57 - 12448736 * q^58 - 1835940 * q^59 - 6364808 * q^60 - 4559780 * q^61 + 12948600 * q^62 + 10001872 * q^63 + 16915544 * q^64 - 8 * q^65 - 11246068 * q^66 - 1940684 * q^67 - 8895536 * q^68 + 9580892 * q^69 - 8149480 * q^70 - 12348708 * q^71 + 12884564 * q^72 - 4 * q^73 + 10931436 * q^74 + 11573008 * q^75 + 14443516 * q^76 - 11914452 * q^77 - 38252364 * q^78 - 11333192 * q^80 + 15827196 * q^82 - 9565884 * q^83 + 8101984 * q^84 + 312496 * q^85 - 14812992 * q^86 + 40789108 * q^87 + 5716448 * q^88 - 4 * q^89 + 5335400 * q^90 - 3406996 * q^91 + 27562664 * q^92 - 8752 * q^93 - 14227032 * q^94 - 54872008 * q^95 - 25080448 * q^96 - 8 * q^97 + 57598104 * q^98 - 9738480 * q^99

Decomposition of \(S_{8}^{\mathrm{new}}(32, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.8.g.a	$32$	$8$	32.g	32.g	$8$	$108$	$27$	$9.996$		None		✓	✓	✓	32.8.g.a	$2$	$0$	\(-4\)	\(-4\)	\(-4\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$