Space of modular forms of level 520, weight 1, and Character 520.b

• Label: 520.1.b
• Level: $520$
• Weight: $1$
• Character orbit: 520.b
• Rep. character: $\chi_{520}(259,\cdot)$
• Character field: $\Q$
• Dimension: $6$
• Newform subspaces: $2$
• Sturm bound: $84$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	520.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 520 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(84\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(520, [\chi])\).

	Total	New	Old
Modular forms	10	10	0
Cusp forms	6	6	0
Eisenstein series	4	4	0

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

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	6	0	0	0

Trace form

\( 6 q - 6 q^{4} - 6 q^{9} + O(q^{10}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(520, [\chi])\) 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
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
520.1.b.a	$520$	$1$	520.b	520.b	$2$	$2$	$2$	$0.260$	\(\Q(\sqrt{-1}) \)	$D_{2}$	\(\Q(\sqrt{-10}) \), \(\Q(\sqrt{-26}) \)	\(\Q(\sqrt{65}) \)		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-iq^{2}-q^{4}+iq^{5}-iq^{7}+iq^{8}+\cdots\)
520.1.b.b	$520$	$1$	520.b	520.b	$2$	$4$	$4$	$0.260$	\(\Q(\zeta_{12})\)	$D_{6}$	\(\Q(\sqrt{-26}) \)	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q-\zeta_{12}^{3}q^{2}+(-\zeta_{12}^{2}-\zeta_{12}^{4})q^{3}+\cdots\)