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

• Label: 3332.1.w
• Level: $3332$
• Weight: $1$
• Character orbit: 3332.w
• Rep. character: $\chi_{3332}(491,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $16$
• Newform subspaces: $4$
• Sturm bound: $504$
• Trace bound: $20$

Defining parameters

Level:	\( N \)	\(=\)	\( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3332.w (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 68 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(504\)
Trace bound:			\(20\)

Dimensions

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

	Total	New	Old
Modular forms	80	56	24
Cusp forms	16	16	0
Eisenstein series	64	40	24

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q - 16 q^{16} - 16 q^{53} + 16 q^{74}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3332.1.w.a	$3332$	$1$	3332.w	68.g	$8$	$4$	$1$	$1.663$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		✓			3332.1.w.a	$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-1-\zeta_{8}^{3})q^{5}+\cdots\)
3332.1.w.b	$3332$	$1$	3332.w	68.g	$8$	$4$	$1$	$1.663$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		✓			3332.1.w.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(\zeta_{8}+\zeta_{8}^{2})q^{5}+\cdots\)
3332.1.w.c	$3332$	$1$	3332.w	68.g	$8$	$4$	$1$	$1.663$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		✓			3332.1.w.b	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(-\zeta_{8}-\zeta_{8}^{2})q^{5}+\cdots\)
3332.1.w.d	$3332$	$1$	3332.w	68.g	$8$	$4$	$1$	$1.663$	\(\Q(\zeta_{8})\)	$D_{8}$	\(\Q(\sqrt{-1}) \)	None		✓			3332.1.w.a	$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{8}q^{2}+\zeta_{8}^{2}q^{4}+(1+\zeta_{8}^{3})q^{5}-\zeta_{8}^{3}q^{8}+\cdots\)