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

• Label: 510.2.z
• Level: $510$
• Weight: $2$
• Character orbit: 510.z
• Rep. character: $\chi_{510}(53,\cdot)$
• Character field: $\Q(\zeta_{8})$
• Dimension: $144$
• Newform subspaces: $4$
• Sturm bound: $216$
• Trace bound: $6$

Defining parameters

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.z (of order \(8\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 255 \)
Character field:			\(\Q(\zeta_{8})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(216\)
Trace bound:			\(6\)
Distinguishing \(T_p\):			\(7\), \(11\)

Dimensions

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

	Total	New	Old
Modular forms	464	144	320
Cusp forms	400	144	256
Eisenstein series	64	0	64

Trace form

144 * q - 144 * q^4 + 16 * q^13 + 24 * q^15 + 144 * q^16 + 16 * q^22 + 16 * q^25 - 48 * q^27 + 16 * q^31 + 16 * q^39 + 24 * q^45 + 32 * q^49 + 16 * q^51 - 16 * q^52 + 16 * q^55 - 64 * q^57 - 16 * q^58 - 24 * q^60 - 32 * q^63 - 144 * q^64 - 16 * q^67 - 48 * q^70 - 80 * q^73 + 80 * q^79 - 32 * q^82 - 80 * q^85 - 80 * q^87 - 16 * q^88 + 24 * q^90 - 96 * q^91 - 112 * q^93 - 16 * q^97 + 48 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
510.2.z.a	$510$	$2$	510.z	255.v	$8$	$4$	$1$	$4.072$	\(\Q(\zeta_{8})\)	None		✓			510.2.w.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q+\zeta_{8}^{2}q^{2}+(1+\zeta_{8}^{2}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
510.2.z.b	$510$	$2$	510.z	255.v	$8$	$4$	$1$	$4.072$	\(\Q(\zeta_{8})\)	None		✓			510.2.w.a	$2$	$0$	\(0\)	\(4\)	\(0\)	\(4\)	$1$	$\mathrm{SU}(2)[C_{8}]$	\(q-\zeta_{8}^{2}q^{2}+(1-\zeta_{8}-\zeta_{8}^{3})q^{3}-q^{4}+\cdots\)
510.2.z.c	$510$	$2$	510.z	255.v	$8$	$68$	$17$	$4.072$		None		✓			510.2.w.c	$2$	$0$	\(0\)	\(-4\)	\(-8\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$
510.2.z.d	$510$	$2$	510.z	255.v	$8$	$68$	$17$	$4.072$		None		✓			510.2.w.c	$2$	$0$	\(0\)	\(-4\)	\(8\)	\(-4\)		$\mathrm{SU}(2)[C_{8}]$

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

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