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

• Label: 816.2.e
• Level: $816$
• Weight: $2$
• Character orbit: 816.e
• Rep. character: $\chi_{816}(239,\cdot)$
• Character field: $\Q$
• Dimension: $32$
• Newform subspaces: $3$
• Sturm bound: $288$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 816 = 2^{4} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	816.e (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 12 \)
Character field:			\(\Q\)
Newform subspaces:			\( 3 \)
Sturm bound:			\(288\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(5\)

Dimensions

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

	Total	New	Old
Modular forms	156	32	124
Cusp forms	132	32	100
Eisenstein series	24	0	24

Trace form

\( 32 q + O(q^{10}) \)

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.e.a	$816$	$2$	816.e	12.b	$2$	$4$	$4$	$6.516$	\(\Q(\zeta_{12})\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{2}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\zeta_{12}^{3}q^{3}+3\zeta_{12}q^{5}+2\zeta_{12}^{2}q^{7}+\cdots\)
816.2.e.b	$816$	$2$	816.e	12.b	$2$	$8$	$8$	$6.516$	8.0.\(\cdots\).8	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{6}q^{3}+2\beta _{3}q^{5}+(-\beta _{1}+\beta _{5})q^{7}+\cdots\)
816.2.e.c	$816$	$2$	816.e	12.b	$2$	$20$	$20$	$6.516$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$2^{16}$	$\mathrm{SU}(2)[C_{2}]$	\(q-\beta _{14}q^{3}-\beta _{15}q^{5}-\beta _{16}q^{7}+(\beta _{9}+\cdots)q^{9}+\cdots\)

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

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