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

• Label: 1368.1.i
• Level: $1368$
• Weight: $1$
• Character orbit: 1368.i
• Rep. character: $\chi_{1368}(37,\cdot)$
• Character field: $\Q$
• Dimension: $2$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1368 = 2^{3} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1368.i (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 152 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	16	4	12
Cusp forms	8	2	6
Eisenstein series	8	2	6

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	2	0	0	0

Trace form

\( 2 q + 2 q^{4} - 2 q^{7} + O(q^{10}) \)

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.i.a	$1368$	$1$	1368.i	152.g	$2$	$1$	$1$	$0.683$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None	✓	$2$	$0$	\(-1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q-q^{2}+q^{4}-q^{7}-q^{8}-q^{13}+q^{14}+\cdots\)
1368.1.i.b	$1368$	$1$	1368.i	152.g	$2$	$1$	$1$	$0.683$	\(\Q\)	$D_{3}$	\(\Q(\sqrt{-38}) \)	None	✓	$2$	$0$	\(1\)	\(0\)	\(0\)	\(-1\)	$1$		\(q+q^{2}+q^{4}-q^{7}+q^{8}+q^{13}-q^{14}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(1368, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(1368, [\chi]) \cong \)