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

• Label: 816.2.cj
• Level: $816$
• Weight: $2$
• Character orbit: 816.cj
• Rep. character: $\chi_{816}(65,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $272$
• Newform subspaces: $6$
• Sturm bound: $288$
• Trace bound: $11$

Defining parameters

Level:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.cj (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 51 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 6 \)
Sturm bound:			\(288\)
Trace bound:			\(11\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	1248	304	944
Cusp forms	1056	272	784
Eisenstein series	192	32	160

Trace form

\( 272 q + 8 q^{3} + 16 q^{7} - 8 q^{9} + O(q^{10}) \)

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	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
816.2.cj.a	$816$	$2$	816.cj	51.i	$16$	$24$	$3$	$6.516$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
816.2.cj.b	$816$	$2$	816.cj	51.i	$16$	$24$	$3$	$6.516$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
816.2.cj.c	$816$	$2$	816.cj	51.i	$16$	$32$	$4$	$6.516$		None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(16\)		$\mathrm{SU}(2)[C_{16}]$
816.2.cj.d	$816$	$2$	816.cj	51.i	$16$	$48$	$6$	$6.516$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
816.2.cj.e	$816$	$2$	816.cj	51.i	$16$	$72$	$9$	$6.516$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
816.2.cj.f	$816$	$2$	816.cj	51.i	$16$	$72$	$9$	$6.516$		None		$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

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

\( S_{2}^{\mathrm{old}}(816, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(102, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(204, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(408, [\chi])\)\(^{\oplus 2}\)