Space of modular forms of level 520, weight 2, and Character 520.t

• Label: 520.2.t
• Level: $520$
• Weight: $2$
• Character orbit: 520.t
• Rep. character: $\chi_{520}(99,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $160$
• Newform subspaces: $3$
• Sturm bound: $168$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.t (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 520 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(520, [\chi])\).

	Total	New	Old
Modular forms	176	176	0
Cusp forms	160	160	0
Eisenstein series	16	16	0

Trace form

\( 160 q + 4 q^{6} - 160 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(520, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
520.2.t.a	$520$	$2$	520.t	520.t	$4$	$4$	$2$	$4.152$	\(\Q(i, \sqrt{10})\)	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(-1-\beta _{2})q^{2}+2\beta _{2}q^{4}+\beta _{1}q^{5}+\cdots\)
520.2.t.b	$520$	$2$	520.t	520.t	$4$	$4$	$2$	$4.152$	\(\Q(i, \sqrt{10})\)	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(4\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{4}]$	\(q+(1-\beta _{2})q^{2}-2\beta _{2}q^{4}-\beta _{3}q^{5}+2\beta _{1}q^{7}+\cdots\)
520.2.t.c	$520$	$2$	520.t	520.t	$4$	$152$	$76$	$4.152$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$