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

• Label: 816.2.bm
• Level: $816$
• Weight: $2$
• Character orbit: 816.bm
• Rep. character: $\chi_{816}(251,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $280$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $2$

Defining parameters

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

Dimensions

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

	Total	New	Old
Modular forms	296	296	0
Cusp forms	280	280	0
Eisenstein series	16	16	0

Trace form

\( 280 q - 8 q^{4} - 6 q^{6} - 8 q^{7} + O(q^{10}) \)

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.bm.a	$816$	$2$	816.bm	816.am	$4$	$4$	$2$	$6.516$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(-4\)	\(-2\)	\(4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(-1+\beta _{2})q^{2}+(-1+\beta _{3})q^{3}-2\beta _{2}q^{4}+\cdots\)
816.2.bm.b	$816$	$2$	816.bm	816.am	$4$	$4$	$2$	$6.516$	\(\Q(i, \sqrt{5})\)	None		$2$	$0$	\(4\)	\(2\)	\(-4\)	\(0\)	$2$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+\beta _{2})q^{2}+(1-\beta _{3})q^{3}+2\beta _{2}q^{4}+\cdots\)
816.2.bm.c	$816$	$2$	816.bm	816.am	$4$	$272$	$136$	$6.516$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(-8\)		$\mathrm{SU}(2)[C_{4}]$