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

• Label: 3328.1.j
• Level: $3328$
• Weight: $1$
• Character orbit: 3328.j
• Rep. character: $\chi_{3328}(385,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• 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.j (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
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	76	12	64
Cusp forms	28	4	24
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	0	0

Trace form

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

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.j.a	$3328$	$1$	3328.j	104.j	$4$	$2$	$1$	$1.661$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None					416.1.t.a	$4$	$0$	\(0\)	\(0\)	\(-2\)	\(0\)	$1$		\(q+(-i-1)q^{5}+q^{9}+q^{13}+2 i q^{17}+\cdots\)
3328.1.j.b	$3328$	$1$	3328.j	104.j	$4$	$2$	$1$	$1.661$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None					416.1.t.a	$4$	$0$	\(0\)	\(0\)	\(2\)	\(0\)	$1$		\(q+(i+1)q^{5}+q^{9}-q^{13}+2 i q^{17}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3328, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(1664, [\chi])\)\(^{\oplus 2}\)