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

• Label: 3328.1.bl
• Level: $3328$
• Weight: $1$
• Character orbit: 3328.bl
• Rep. character: $\chi_{3328}(513,\cdot)$
• Character field: $\Q(\zeta_{12})$
• 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.bl (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{12})\)
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	132	24	108
Cusp forms	36	8	28
Eisenstein series	96	16	80

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

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

Trace form

\( 8 q + 4 q^{9} + 8 q^{41} + 8 q^{65} - 4 q^{73} - 4 q^{81} + 4 q^{89} + 4 q^{97}+O(q^{100}) \)

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3328.1.bl.a	$3328$	$1$	3328.bl	13.f	$12$	$4$	$1$	$1.661$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None					1664.1.bv.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(-\zeta_{12}-\zeta_{12}^{2})q^{5}+\zeta_{12}^{2}q^{9}+\zeta_{12}^{4}q^{13}+\cdots\)
3328.1.bl.b	$3328$	$1$	3328.bl	13.f	$12$	$4$	$1$	$1.661$	\(\Q(\zeta_{12})\)	$D_{12}$	\(\Q(\sqrt{-1}) \)	None					1664.1.bv.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(\zeta_{12}+\zeta_{12}^{2})q^{5}+\zeta_{12}^{2}q^{9}-\zeta_{12}^{4}q^{13}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(3328, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(3328, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(832, [\chi])\)\(^{\oplus 3}\)