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

• Label: 510.2.bi
• Level: $510$
• Weight: $2$
• Character orbit: 510.bi
• Rep. character: $\chi_{510}(37,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $144$
• Newform subspaces: $2$
• Sturm bound: $216$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bi (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 85 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(216\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(7\)

Dimensions

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

	Total	New	Old
Modular forms	928	144	784
Cusp forms	800	144	656
Eisenstein series	128	0	128

Trace form

144 * q + 16 * q^10 + 32 * q^25 + 32 * q^28 + 32 * q^31 - 32 * q^33 - 32 * q^34 + 32 * q^37 + 80 * q^41 + 64 * q^50 + 32 * q^52 - 64 * q^53 + 32 * q^55 + 64 * q^57 - 64 * q^59 - 32 * q^67 - 32 * q^70 - 64 * q^71 - 16 * q^72 - 80 * q^73 - 80 * q^74 - 64 * q^75 - 96 * q^77 - 64 * q^78 - 32 * q^80 - 64 * q^83 - 96 * q^85 - 64 * q^86 - 96 * q^87 - 32 * q^88 - 32 * q^92 - 96 * q^93 + 32 * q^97 - 144 * q^98

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.bi.a	$510$	$2$	510.bi	85.r	$16$	$64$	$8$	$4.072$		None		✓			510.2.bd.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
510.2.bi.b	$510$	$2$	510.bi	85.r	$16$	$80$	$10$	$4.072$		None		✓	✓		510.2.bd.b	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

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

\( S_{2}^{\mathrm{old}}(510, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(85, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(170, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(255, [\chi])\)\(^{\oplus 2}\)