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

• Label: 1352.1.n
• Level: $1352$
• Weight: $1$
• Character orbit: 1352.n
• Rep. character: $\chi_{1352}(315,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $16$
• 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.n (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 104 \)
Character field:			\(\Q(\zeta_{6})\)
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	44	36	8
Cusp forms	16	16	0
Eisenstein series	28	20	8

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	16	0	0	0

Trace form

\( 16 q + 4 q^{3} - 4 q^{4} - 4 q^{9} + O(q^{10}) \)

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.n.a	$1352$	$1$	1352.n	104.n	$6$	$4$	$2$	$0.675$	\(\Q(\zeta_{12})\)	$D_{3}$	\(\Q(\sqrt{-26}) \)	None		$8$	$0$	\(0\)	\(2\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}q^{2}-\zeta_{12}^{4}q^{3}+\zeta_{12}^{2}q^{4}-\zeta_{12}^{3}q^{5}+\cdots\)
1352.1.n.b	$1352$	$1$	1352.n	104.n	$6$	$6$	$3$	$0.675$	6.0.64827.1	$D_{7}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(-3\)	\(1\)	\(0\)	\(0\)	$1$		\(q-\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)
1352.1.n.c	$1352$	$1$	1352.n	104.n	$6$	$6$	$3$	$0.675$	6.0.64827.1	$D_{7}$	\(\Q(\sqrt{-2}) \)	None		$4$	$0$	\(3\)	\(1\)	\(0\)	\(0\)	$1$		\(q+\beta _{5}q^{2}+(\beta _{1}-\beta _{2}+\beta _{3}+\beta _{4}+\beta _{5})q^{3}+\cdots\)