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

• Label: 520.2.cz
• Level: $520$
• Weight: $2$
• Character orbit: 520.cz
• Rep. character: $\chi_{520}(19,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $320$
• 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.cz (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 520 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(168\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	352	352	0
Cusp forms	320	320	0
Eisenstein series	32	32	0

Trace form

\( 320 q - 12 q^{4} - 16 q^{6} + 136 q^{9} + O(q^{10}) \)

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.cz.a	$520$	$2$	520.cz	520.bz	$12$	$8$	$2$	$4.152$	8.0.3317760000.2	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(-4\)	\(0\)	\(0\)	\(12\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(-1+\beta _{2}+\beta _{4})q^{2}+(-2\beta _{2}+2\beta _{6}+\cdots)q^{4}+\cdots\)
520.2.cz.b	$520$	$2$	520.cz	520.bz	$12$	$8$	$2$	$4.152$	8.0.3317760000.2	\(\Q(\sqrt{-10}) \)		$4$	$0$	\(4\)	\(0\)	\(0\)	\(-12\)	$1$	$\mathrm{U}(1)[D_{12}]$	\(q+(1-\beta _{2}-\beta _{4})q^{2}+(-2\beta _{2}+2\beta _{6}+\cdots)q^{4}+\cdots\)
520.2.cz.c	$520$	$2$	520.cz	520.bz	$12$	$304$	$76$	$4.152$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{12}]$