Space of modular forms of level 3332, weight 1, and Character 3332.bn

• Label: 3332.1.bn
• Level: $3332$
• Weight: $1$
• Character orbit: 3332.bn
• Rep. character: $\chi_{3332}(979,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $32$
• Newform subspaces: $4$
• Sturm bound: $504$
• Trace bound: $18$

Defining parameters

Level:	\( N \)	\(=\)	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3332.bn (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 476 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(504\)
Trace bound:			\(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3332, [\chi])\).

	Total	New	Old
Modular forms	160	96	64
Cusp forms	32	32	0
Eisenstein series	128	64	64

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	32	0	0	0

Trace form

\( 32 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3332, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3332.1.bn.a	$3332$	$1$	3332.bn	476.af	$16$	$8$	$1$	$1.663$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(-\zeta_{16}^{2}+\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
3332.1.bn.b	$3332$	$1$	3332.bn	476.af	$16$	$8$	$1$	$1.663$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(-\zeta_{16}+\zeta_{16}^{6}+\cdots)q^{5}+\cdots\)
3332.1.bn.c	$3332$	$1$	3332.bn	476.af	$16$	$8$	$1$	$1.663$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(\zeta_{16}^{2}-\zeta_{16}^{5}+\cdots)q^{5}+\cdots\)
3332.1.bn.d	$3332$	$1$	3332.bn	476.af	$16$	$8$	$1$	$1.663$	\(\Q(\zeta_{16})\)	$D_{16}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{16}^{5}q^{2}-\zeta_{16}^{2}q^{4}+(\zeta_{16}-\zeta_{16}^{6}+\cdots)q^{5}+\cdots\)