Space of modular forms of level 3381, weight 1, and Character 3381.c

• Label: 3381.1.c
• Level: $3381$
• Weight: $1$
• Character orbit: 3381.c
• Rep. character: $\chi_{3381}(3380,\cdot)$
• Character field: $\Q$
• Dimension: $24$
• Newform subspaces: $2$
• Sturm bound: $448$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 3381 = 3 \cdot 7^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3381.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 483 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(448\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3381, [\chi])\).

	Total	New	Old
Modular forms	40	32	8
Cusp forms	24	24	0
Eisenstein series	16	8	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	24	0	0	0

Trace form

\( 24 q - 24 q^{4} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(3381, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3381.1.c.a	$3381$	$1$	3381.c	483.c	$2$	$8$	$8$	$1.687$	\(\Q(\zeta_{16})\)	$D_{8}$	\(\Q(\sqrt{-23}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(\zeta_{16}^{2}+\zeta_{16}^{6})q^{2}-\zeta_{16}q^{3}-q^{4}+\cdots\)
3381.1.c.b	$3381$	$1$	3381.c	483.c	$2$	$16$	$16$	$1.687$	\(\Q(\zeta_{48})\)	$D_{24}$	\(\Q(\sqrt{-23}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{48}^{2}-\zeta_{48}^{22})q^{2}+\zeta_{48}^{5}q^{3}+\cdots\)