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

• Label: 510.2.p
• Level: $510$
• Weight: $2$
• Character orbit: 510.p
• Rep. character: $\chi_{510}(361,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $24$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.p (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 17 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	232	24	208
Cusp forms	200	24	176
Eisenstein series	32	0	32

Trace form

\( 24 q - 24 q^{4} + O(q^{10}) \)

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.p.a	$510$	$2$	510.p	17.c	$4$	$4$	$2$	$4.072$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}+\zeta_{8}q^{5}-\zeta_{8}^{3}q^{6}+\cdots\)
510.2.p.b	$510$	$2$	510.p	17.c	$4$	$4$	$2$	$4.072$	\(\Q(\zeta_{8})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(8\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+\zeta_{8}^{2}q^{2}+\zeta_{8}q^{3}-q^{4}-\zeta_{8}q^{5}+\zeta_{8}^{3}q^{6}+\cdots\)
510.2.p.c	$510$	$2$	510.p	17.c	$4$	$8$	$4$	$4.072$	8.0.18939904.2	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{4}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\beta _{4}q^{2}+\beta _{2}q^{3}-q^{4}-\beta _{2}q^{5}-\beta _{3}q^{6}+\cdots\)
510.2.p.d	$510$	$2$	510.p	17.c	$4$	$8$	$4$	$4.072$	\(\Q(\zeta_{16})\)	None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{3}$	$\mathrm{SU}(2)[C_{4}]$	\(q-\zeta_{16}^{2}q^{2}+\zeta_{16}^{4}q^{3}-q^{4}+\zeta_{16}^{4}q^{5}+\cdots\)

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

\( S_{2}^{\mathrm{old}}(510, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(34, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 2}\)