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

• Label: 32.8.b
• Level: $32$
• Weight: $8$
• Character orbit: 32.b
• Rep. character: $\chi_{32}(17,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $32$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	32.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
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	32	8	24
Cusp forms	24	6	18
Eisenstein series	8	2	6

Trace form

6 * q + 688 * q^7 - 2918 * q^9 - 17872 * q^15 + 1452 * q^17 + 1296 * q^23 - 39314 * q^25 + 89280 * q^31 + 53880 * q^33 + 328208 * q^39 + 521244 * q^41 - 1566432 * q^47 - 511050 * q^49 + 3270256 * q^55 - 1889896 * q^57 - 5776816 * q^63 + 1416480 * q^65 + 7597104 * q^71 + 2089564 * q^73 - 16015904 * q^79 - 723058 * q^81 + 37453776 * q^87 + 2169084 * q^89 - 48537936 * q^95 - 1088308 * q^97

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.b.a	$32$	$8$	32.b	8.b	$2$	$6$	$6$	$9.996$	\(\mathbb{Q}[x]/(x^{6} - \cdots)\)	None			✓	✓	8.8.b.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(688\)	$2^{30}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{2}q^{3}+(\beta _{2}+\beta _{3})q^{5}+(115+\beta _{1}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{8}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{8}^{\mathrm{old}}(32, [\chi]) \simeq \) \(S_{8}^{\mathrm{new}}(8, [\chi])\)\(^{\oplus 3}\)