Space of modular forms of level 260, weight 1, and Character 260.s

• Label: 260.1.s
• Level: $260$
• Weight: $1$
• Character orbit: 260.s
• Rep. character: $\chi_{260}(187,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $2$
• Newform subspaces: $1$
• Sturm bound: $42$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	260.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 260 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(42\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(260, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	2	2	0
Eisenstein series	8	8	0

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

\( 2 q - 2 q^{2} + 2 q^{4} - 2 q^{8} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(260, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
260.1.s.a	$260$	$1$	260.s	260.s	$4$	$2$	$1$	$0.130$	\(\Q(\sqrt{-1}) \)	$D_{4}$	\(\Q(\sqrt{-1}) \)	None		$4$	$0$	\(-2\)	\(0\)	\(0\)	\(0\)	$1$		\(q-q^{2}+q^{4}+iq^{5}-q^{8}+iq^{9}-iq^{10}+\cdots\)