Space of modular forms of level 32, weight 3, and Character 32.c

• Label: 32.3.c
• Level: $32$
• Weight: $3$
• Character orbit: 32.c
• Rep. character: $\chi_{32}(31,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $12$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 32 = 2^{5} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	32.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 4 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(12\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(32, [\chi])\).

	Total	New	Old
Modular forms	12	2	10
Cusp forms	4	2	2
Eisenstein series	8	0	8

Trace form

\( 2 q + 4 q^{5} - 14 q^{9} + O(q^{10}) \)

Decomposition of \(S_{3}^{\mathrm{new}}(32, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
32.3.c.a	$32$	$3$	32.c	4.b	$2$	$2$	$2$	$0.872$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+iq^{3}+2q^{5}-2iq^{7}-7q^{9}-iq^{11}+\cdots\)

Decomposition of \(S_{3}^{\mathrm{old}}(32, [\chi])\) into lower level spaces

\( S_{3}^{\mathrm{old}}(32, [\chi]) \cong \) \(S_{3}^{\mathrm{new}}(16, [\chi])\)\(^{\oplus 2}\)