Space of modular forms of level 1352, weight 1, and Character 1352.g

• Label: 1352.1.g
• Level: $1352$
• Weight: $1$
• Character orbit: 1352.g
• Rep. character: $\chi_{1352}(339,\cdot)$
• Character field: $\Q$
• Dimension: $8$
• Newform subspaces: $3$
• Sturm bound: $182$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 1352 = 2^{3} \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	1352.g (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 8 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(182\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(1352, [\chi])\).

	Total	New	Old
Modular forms	22	19	3
Cusp forms	8	8	0
Eisenstein series	14	11	3

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

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

Trace form

\( 8 q - 4 q^{3} + 4 q^{4} + 4 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(1352, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
1352.1.g.a	$1352$	$1$	1352.g	8.d	$2$	$2$	$2$	$0.675$	\(\Q(\sqrt{-1}) \)	$D_{3}$	\(\Q(\sqrt{-26}) \)	None		$4$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-q^{3}-q^{4}+iq^{5}+iq^{6}-iq^{7}+\cdots\)
1352.1.g.b	$1352$	$1$	1352.g	8.d	$2$	$3$	$3$	$0.675$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2}) \)	None	✓	$2$	$0$	\(-3\)	\(-1\)	\(0\)	\(0\)	$1$		\(q-q^{2}-\beta _{1}q^{3}+q^{4}+\beta _{1}q^{6}-q^{8}+\cdots\)
1352.1.g.c	$1352$	$1$	1352.g	8.d	$2$	$3$	$3$	$0.675$	\(\Q(\zeta_{14})^+\)	$D_{7}$	\(\Q(\sqrt{-2}) \)	None	✓	$2$	$0$	\(3\)	\(-1\)	\(0\)	\(0\)	$1$		\(q+q^{2}-\beta _{1}q^{3}+q^{4}-\beta _{1}q^{6}+q^{8}+\cdots\)