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

• Label: 816.2.s
• Level: $816$
• Weight: $2$
• Character orbit: 816.s
• Rep. character: $\chi_{816}(157,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $144$
• Newform subspaces: $4$
• Sturm bound: $288$
• Trace bound: $7$

Defining parameters

Level:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 272 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(288\)
Trace bound:			\(7\)
Distinguishing \(T_p\):			\(5\), \(7\)

Dimensions

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

	Total	New	Old
Modular forms	296	144	152
Cusp forms	280	144	136
Eisenstein series	16	0	16

Trace form

\( 144 q + 4 q^{6} + 144 q^{9} + O(q^{10}) \)

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.s.a	$816$	$2$	816.s	272.s	$4$	$2$	$1$	$6.516$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(2\)	\(0\)	\(-2\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\)
816.2.s.b	$816$	$2$	816.s	272.s	$4$	$2$	$1$	$6.516$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(2\)	\(2\)	\(0\)	\(6\)	$1$	$\mathrm{SU}(2)[C_{4}]$	\(q+(1+i)q^{2}+q^{3}+2iq^{4}+(1+i)q^{6}+\cdots\)
816.2.s.c	$816$	$2$	816.s	272.s	$4$	$68$	$34$	$6.516$		None		$2$	$0$	\(-2\)	\(68\)	\(0\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$
816.2.s.d	$816$	$2$	816.s	272.s	$4$	$72$	$36$	$6.516$		None		$2$	$0$	\(-2\)	\(-72\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{4}]$

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

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