Space of modular forms of level 510, weight 2, and Character 510.q

• Label: 510.2.q
• Level: $510$
• Weight: $2$
• Character orbit: 510.q
• Rep. character: $\chi_{510}(203,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $72$
• Newform subspaces: $1$
• Sturm bound: $216$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.q (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 255 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(216\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(510, [\chi])\).

	Total	New	Old
Modular forms	232	72	160
Cusp forms	200	72	128
Eisenstein series	32	0	32

Trace form

\( 72 q + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(510, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
510.2.q.a	$510$	$2$	510.q	255.o	$4$	$72$	$36$	$4.072$		None		$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

Decomposition of \(S_{2}^{\mathrm{old}}(510, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(510, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)