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

• Label: 3328.1.c
• Level: $3328$
• Weight: $1$
• Character orbit: 3328.c
• Rep. character: $\chi_{3328}(3327,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $6$
• Sturm bound: $448$
• Trace bound: $13$

Defining parameters

Level:	\( N \)	\(=\)	\( 3328 = 2^{8} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3328.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 52 \)
Character field:			\(\Q\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(448\)
Trace bound:			\(13\)

Dimensions

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

	Total	New	Old
Modular forms	46	18	28
Cusp forms	22	14	8
Eisenstein series	24	4	20

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	14	0	0	0

Trace form

\( 14 q - 2 q^{9} + O(q^{10}) \)

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.c.a	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-26}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-2\)	$1$		\(q-iq^{3}-iq^{5}-q^{7}-iq^{13}-q^{15}+\cdots\)
3328.1.c.b	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-13}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\beta q^{7}+q^{9}-\beta q^{11}-q^{13}+\beta q^{19}+\cdots\)
3328.1.c.c	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-1}) \), \(\Q(\sqrt{-26}) \)	\(\Q(\sqrt{26}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{5}+q^{9}-iq^{13}+q^{17}-3q^{25}+\cdots\)
3328.1.c.d	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	\(\Q(\sqrt{2}) \)	$D_{4}$	\(\Q(\sqrt{-13}) \)	None	✓	$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\beta q^{7}+q^{9}-\beta q^{11}+q^{13}+\beta q^{19}+\cdots\)
3328.1.c.e	$3328$	$1$	3328.c	52.b	$2$	$2$	$2$	$1.661$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-26}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(2\)	$1$		\(q+iq^{3}-iq^{5}+q^{7}-iq^{13}+q^{15}+\cdots\)
3328.1.c.f	$3328$	$1$	3328.c	52.b	$2$	$4$	$4$	$1.661$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-26}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$		\(q+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}-\zeta_{12}^{3}q^{5}+\cdots\)

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

\( S_{1}^{\mathrm{old}}(3328, [\chi]) \cong \)