Space of modular forms of level 32, weight 10, and Character 32.b

• Label: 32.10.b
• Level: $32$
• Weight: $10$
• Character orbit: 32.b
• Rep. character: $\chi_{32}(17,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $40$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 10 \)
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:			\(40\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{10}(32, [\chi])\).

	Total	New	Old
Modular forms	40	10	30
Cusp forms	32	8	24
Eisenstein series	8	2	6

Trace form

\( 8 q - 4800 q^{7} - 39368 q^{9} + O(q^{10}) \)

Decomposition of \(S_{10}^{\mathrm{new}}(32, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.10.b.a	$32$	$10$	32.b	8.b	$2$	$8$	$8$	$16.481$	\(\mathbb{Q}[x]/(x^{8} - \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-4800\)	$2^{56}\cdot 3^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{1}q^{3}+(\beta _{1}-\beta _{2})q^{5}+(-600-\beta _{3}+\cdots)q^{7}+\cdots\)

Decomposition of \(S_{10}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{10}^{\mathrm{old}}(32, [\chi]) \cong \)