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

• Label: 520.2.p
• Level: $520$
• Weight: $2$
• Character orbit: 520.p
• Rep. character: $\chi_{520}(389,\cdot)$
• Character field: $\Q$
• Dimension: $80$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.p (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 520 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(3\)

Dimensions

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

	Total	New	Old
Modular forms	88	88	0
Cusp forms	80	80	0
Eisenstein series	8	8	0

Trace form

\( 80 q - 4 q^{4} + 64 q^{9} + O(q^{10}) \)

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.p.a	$520$	$2$	520.p	520.p	$2$	$8$	$8$	$4.152$	8.0.207360000.1	None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}+(-\beta _{4}+\beta _{7})q^{3}-\beta _{5}q^{4}+\cdots\)
520.2.p.b	$520$	$2$	520.p	520.p	$2$	$72$	$72$	$4.152$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$