Space of modular forms of level 3185, weight 1, and Character 3185.o

• Label: 3185.1.o
• Level: $3185$
• Weight: $1$
• Character orbit: 3185.o
• Rep. character: $\chi_{3185}(99,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $4$
• Newform subspaces: $1$
• Sturm bound: $392$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 3185 = 5 \cdot 7^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	3185.o (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(392\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(3185, [\chi])\).

	Total	New	Old
Modular forms	36	24	12
Cusp forms	4	4	0
Eisenstein series	32	20	12

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	4	0	0	0

Trace form

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

Decomposition of \(S_{1}^{\mathrm{new}}(3185, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
3185.1.o.a	$3185$	$1$	3185.o	65.g	$4$	$4$	$2$	$1.590$	\(\Q(\zeta_{8})\)	$D_{4}$	\(\Q(\sqrt{-35}) \)	None		✓	3185.1.o.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{8}-\zeta_{8}^{3})q^{3}+\zeta_{8}^{2}q^{4}+\zeta_{8}^{3}q^{5}+\cdots\)