Space of modular forms of level 3328, weight 1, and Character 3328.r

• Label: 3328.1.r
• Level: $3328$
• Weight: $1$
• Character orbit: 3328.r
• Rep. character: $\chi_{3328}(2241,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $8$
• Newform subspaces: $2$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3328 = 2^{8} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3328.r (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 208 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(448\)
Trace bound:			\(5\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3328, [\chi])\).

	Total	New	Old
Modular forms	56	8	48
Cusp forms	8	8	0
Eisenstein series	48	0	48

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	8	0

Trace form

\( 8 q + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3328, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3328.1.r.a	$3328$	$1$	3328.r	208.r	$4$	$4$	$2$	$1.661$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{3}-q^{5}+\zeta_{8}^{3}q^{7}-\zeta_{8}^{2}q^{13}+\cdots\)
3328.1.r.b	$3328$	$1$	3328.r	208.r	$4$	$4$	$2$	$1.661$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q-\zeta_{8}^{3}q^{3}+q^{5}-\zeta_{8}^{3}q^{7}+\zeta_{8}^{2}q^{13}+\cdots\)