Space of modular forms of level 816, weight 2, and Character 816.cg

• Label: 816.2.cg
• Level: $816$
• Weight: $2$
• Character orbit: 816.cg
• Rep. character: $\chi_{816}(91,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $576$
• Newform subspaces: $1$
• Sturm bound: $288$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.cg (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 272 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(288\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(816, [\chi])\).

	Total	New	Old
Modular forms	1184	576	608
Cusp forms	1120	576	544
Eisenstein series	64	0	64

Trace form

576 * q + 16 * q^6 - 32 * q^19 - 16 * q^24 + 48 * q^28 + 64 * q^30 + 16 * q^36 - 80 * q^38 - 176 * q^40 + 64 * q^44 + 64 * q^58 - 16 * q^60 + 64 * q^61 - 80 * q^62 - 96 * q^64 + 64 * q^65 + 64 * q^70 - 96 * q^82 + 96 * q^84 + 160 * q^92 + 112 * q^94

Decomposition of \(S_{2}^{\mathrm{new}}(816, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
816.2.cg.a	$816$	$2$	816.cg	272.ad	$16$	$576$	$72$	$6.516$		None		✓	✓	✓	816.2.cg.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(816, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(816, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(272, [\chi])\)\(^{\oplus 2}\)