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

• Label: 3328.1.t
• Level: $3328$
• Weight: $1$
• Character orbit: 3328.t
• Rep. character: $\chi_{3328}(2049,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $12$
• Newform subspaces: $4$
• Sturm bound: $448$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 3328 = 2^{8} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3328.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
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	74	20	54
Cusp forms	26	12	14
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

\( 12 q - 4 q^{9} - 8 q^{33} + 4 q^{41} + 4 q^{65} + 4 q^{73} - 4 q^{81} - 4 q^{89} - 12 q^{97}+O(q^{100}) \)

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.t.a	$3328$	$1$	3328.t	13.d	$4$	$2$	$1$	$1.661$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None					1664.1.j.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(i-1)q^{5}-q^{9}-q^{13}-2 i q^{17}+\cdots\)
3328.1.t.b	$3328$	$1$	3328.t	13.d	$4$	$2$	$1$	$1.661$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None					1664.1.j.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(-i+1)q^{5}-q^{9}+q^{13}-2 i q^{17}+\cdots\)
3328.1.t.c	$3328$	$1$	3328.t	13.d	$4$	$4$	$2$	$1.661$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None					1664.1.j.c	$4$	$0$	\(0\)	\(-4\)	\(0\)	\(0\)	$1$		\(q-q^{3}-\zeta_{8}q^{5}-\zeta_{8}^{3}q^{7}+(1-\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)
3328.1.t.d	$3328$	$1$	3328.t	13.d	$4$	$4$	$2$	$1.661$	\(\Q(\zeta_{8})\)	$S_{4}$	None	None					1664.1.j.c	$4$	$0$	\(0\)	\(4\)	\(0\)	\(0\)	$1$		\(q+q^{3}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{7}+(-1+\zeta_{8}^{2}+\cdots)q^{11}+\cdots\)

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

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