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

• Label: 3328.1.bb
• Level: $3328$
• Weight: $1$
• Character orbit: 3328.bb
• Rep. character: $\chi_{3328}(1023,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $12$
• Newform subspaces: $3$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3328 = 2^{8} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3328.bb (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 3 \)
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	108	20	88
Cusp forms	60	12	48
Eisenstein series	48	8	40

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	8	0

Trace form

\( 12 q + 2 q^{9} + O(q^{10}) \)

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.bb.a	$3328$	$1$	3328.bb	52.j	$6$	$4$	$2$	$1.661$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(-4\)	\(0\)	$1$		\(q+(\beta _{1}-\beta _{3})q^{3}-q^{5}+(1-\beta _{2})q^{9}+\beta _{2}q^{13}+\cdots\)
3328.1.bb.b	$3328$	$1$	3328.bb	52.j	$6$	$4$	$2$	$1.661$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-1}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{12}-\zeta_{12}^{5})q^{5}-\zeta_{12}^{2}q^{9}-\zeta_{12}q^{13}+\cdots\)
3328.1.bb.c	$3328$	$1$	3328.bb	52.j	$6$	$4$	$2$	$1.661$	\(\Q(\sqrt{-2}, \sqrt{-3})\)	$S_{4}$	None	None		$4$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$		\(q+(\beta _{1}-\beta _{3})q^{3}+q^{5}+(1-\beta _{2})q^{9}-\beta _{2}q^{13}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3328, [\chi]) \cong \) \(S_{1}^{\mathrm{new}}(52, [\chi])\)\(^{\oplus 7}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(104, [\chi])\)\(^{\oplus 6}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(208, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{1}^{\mathrm{new}}(416, [\chi])\)\(^{\oplus 4}\)