Space of modular forms of level 1368, weight 1, and Character 1368.bw

• Label: 1368.1.bw
• Level: $1368$
• Weight: $1$
• Character orbit: 1368.bw
• Rep. character: $\chi_{1368}(125,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1368.bw (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 456 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1368, [\chi])\).

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

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

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

Trace form

\( 8 q - 8 q^{7} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1368, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1368.1.bw.a	$1368$	$1$	1368.bw	456.x	$6$	$8$	$4$	$0.683$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$		\(q-\zeta_{24}^{5}q^{2}+\zeta_{24}^{10}q^{4}-q^{7}+\zeta_{24}^{3}q^{8}+\cdots\)