Space of modular forms of level 32, weight 6, and Character 32.g

• Label: 32.6.g
• Level: $32$
• Weight: $6$
• Character orbit: 32.g
• Rep. character: $\chi_{32}(5,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $76$
• Newform subspaces: $1$
• Sturm bound: $24$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 6 \)
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:			\(24\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(32, [\chi])\).

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

Trace form

76 * 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 - 204 * q^10 - 4 * q^11 - 1588 * q^12 - 4 * q^13 + 2476 * q^14 + 4176 * q^16 - 1624 * q^18 - 4 * q^19 - 7604 * q^20 - 4 * q^21 - 12384 * q^22 + 1668 * q^23 + 21456 * q^24 - 4 * q^25 + 12976 * q^26 - 7468 * q^27 - 2184 * q^28 - 4 * q^29 - 32316 * q^30 + 23056 * q^31 - 18584 * q^32 - 8 * q^33 - 6256 * q^34 - 4780 * q^35 + 65584 * q^36 - 4 * q^37 + 404 * q^38 - 44908 * q^39 - 28952 * q^40 - 4 * q^41 - 53624 * q^42 + 32068 * q^43 + 3716 * q^44 + 968 * q^45 + 63324 * q^46 + 112368 * q^48 - 4524 * q^50 - 19912 * q^51 + 18468 * q^52 - 49460 * q^53 + 1312 * q^54 + 110044 * q^55 - 80984 * q^56 - 4 * q^57 - 84576 * q^58 - 28964 * q^59 - 46088 * q^60 + 96156 * q^61 + 63480 * q^62 - 158768 * q^63 - 49192 * q^64 - 8 * q^65 - 145012 * q^66 - 61164 * q^67 - 151216 * q^68 - 44644 * q^69 - 56296 * q^70 + 143836 * q^71 + 27092 * q^72 - 4 * q^73 + 213100 * q^74 + 205744 * q^75 + 255996 * q^76 - 14900 * q^77 + 83508 * q^78 - 97096 * q^80 + 435196 * q^82 - 329244 * q^83 + 597472 * q^84 + 12496 * q^85 + 269888 * q^86 - 282188 * q^87 - 199840 * q^88 - 4 * q^89 - 706840 * q^90 + 200108 * q^91 - 650328 * q^92 - 976 * q^93 - 261592 * q^94 + 577592 * q^95 - 501376 * q^96 - 8 * q^97 - 395624 * q^98 + 338544 * q^99

Decomposition of \(S_{6}^{\mathrm{new}}(32, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.6.g.a	$32$	$6$	32.g	32.g	$8$	$76$	$19$	$5.132$		None		✓	✓	✓	32.6.g.a	$2$	$0$	\(-4\)	\(-4\)	\(-4\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$