Space of modular forms of level 512, weight 2, and Character 512.i

• Label: 512.2.i
• Level: $512$
• Weight: $2$
• Character orbit: 512.i
• Rep. character: $\chi_{512}(33,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $112$
• Newform subspaces: $2$
• Sturm bound: $128$
• Trace bound: $3$

Defining parameters

Level:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.i (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 64 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(128\)
Trace bound:			\(3\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(512, [\chi])\).

	Total	New	Old
Modular forms	576	144	432
Cusp forms	448	112	336
Eisenstein series	128	32	96

Trace form

112 * q + 16 * q^5 - 16 * q^9 + 16 * q^13 - 16 * q^17 + 16 * q^21 - 16 * q^25 + 16 * q^29 + 16 * q^37 - 16 * q^41 + 16 * q^45 - 16 * q^49 + 16 * q^53 - 16 * q^57 + 16 * q^61 - 32 * q^65 + 16 * q^69 - 16 * q^73 + 16 * q^77 - 16 * q^81 + 16 * q^85 - 16 * q^89 - 32 * q^93

Decomposition of \(S_{2}^{\mathrm{new}}(512, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
512.2.i.a	$512$	$2$	512.i	64.i	$16$	$56$	$7$	$4.088$		None					64.2.i.a	$2$	$0$	\(0\)	\(-8\)	\(8\)	\(8\)		$\mathrm{SU}(2)[C_{16}]$
512.2.i.b	$512$	$2$	512.i	64.i	$16$	$56$	$7$	$4.088$		None					64.2.i.a	$2$	$0$	\(0\)	\(8\)	\(8\)	\(-8\)		$\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(512, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(512, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(64, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(256, [\chi])\)\(^{\oplus 2}\)