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

• Label: 520.2.f
• Level: $520$
• Weight: $2$
• Character orbit: 520.f
• Rep. character: $\chi_{520}(129,\cdot)$
• Character field: $\Q$
• Dimension: $20$
• Newform subspaces: $2$
• Sturm bound: $168$
• Trace bound: $5$

Defining parameters

Level:	\( N \)	\(=\)	\( 520 = 2^{3} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	520.f (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 65 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(168\)
Trace bound:			\(5\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	92	20	72
Cusp forms	76	20	56
Eisenstein series	16	0	16

Trace form

\( 20 q - 16 q^{9} + O(q^{10}) \)

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.f.a	$520$	$2$	520.f	65.d	$2$	$10$	$10$	$4.152$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(-3\)	\(2\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}+\beta _{6}q^{5}-\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)
520.2.f.b	$520$	$2$	520.f	65.d	$2$	$10$	$10$	$4.152$	\(\mathbb{Q}[x]/(x^{10} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(3\)	\(-2\)	$2^{8}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{3}q^{3}-\beta _{6}q^{5}+\beta _{2}q^{7}+(-1-\beta _{1}+\cdots)q^{9}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(520, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(520, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(65, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(130, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(260, [\chi])\)\(^{\oplus 2}\)