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

• Label: 1368.1.dh
• Level: $1368$
• Weight: $1$
• Character orbit: 1368.dh
• Rep. character: $\chi_{1368}(43,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $12$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1368.dh (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 1368 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	36	36	0
Cusp forms	12	12	0
Eisenstein series	24	24	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	12	0	0	0

Trace form

\( 12 q - 3 q^{3} - 3 q^{6} - 6 q^{8} - 3 q^{9} + O(q^{10}) \)

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.dh.a	$1368$	$1$	1368.dh	1368.ch	$18$	$6$	$1$	$0.683$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{6}q^{3}+\zeta_{18}^{8}q^{4}+\cdots\)
1368.1.dh.b	$1368$	$1$	1368.dh	1368.ch	$18$	$6$	$1$	$0.683$	\(\Q(\zeta_{18})\)	$D_{9}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+\zeta_{18}^{4}q^{2}+\zeta_{18}^{8}q^{3}+\zeta_{18}^{8}q^{4}+\cdots\)