Space of modular forms of level 867, weight 2, and Character 867.i

• Label: 867.2.i
• Level: $867$
• Weight: $2$
• Character orbit: 867.i
• Rep. character: $\chi_{867}(65,\cdot)$
• Character field: $\Q(\zeta_{16})$
• Dimension: $608$
• Newform subspaces: $12$
• Sturm bound: $204$
• Trace bound: $10$

Defining parameters

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.i (of order \(16\) and degree \(8\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 51 \)
Character field:			\(\Q(\zeta_{16})\)
Newform subspaces:			\( 12 \)
Sturm bound:			\(204\)
Trace bound:			\(10\)
Distinguishing \(T_p\):			\(2\), \(5\), \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(867, [\chi])\).

	Total	New	Old
Modular forms	960	832	128
Cusp forms	672	608	64
Eisenstein series	288	224	64

Trace form

\( 608 q + 8 q^{3} + 16 q^{4} + 8 q^{6} + 16 q^{7} + 8 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(867, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
867.2.i.a	$867$	$2$	867.i	51.i	$16$	$16$	$2$	$6.923$	16.0.\(\cdots\).2	\(\Q(\sqrt{-51}) \)		$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{16}]$	\(q+\beta _{5}q^{3}+2\beta _{12}q^{4}-\beta _{9}q^{5}+3\beta _{10}q^{9}+\cdots\)
867.2.i.b	$867$	$2$	867.i	51.i	$16$	$32$	$4$	$6.923$		None		$4$	$0$	\(0\)	\(-8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.c	$867$	$2$	867.i	51.i	$16$	$32$	$4$	$6.923$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.d	$867$	$2$	867.i	51.i	$16$	$32$	$4$	$6.923$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.e	$867$	$2$	867.i	51.i	$16$	$32$	$4$	$6.923$		None		$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.f	$867$	$2$	867.i	51.i	$16$	$32$	$4$	$6.923$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.g	$867$	$2$	867.i	51.i	$16$	$32$	$4$	$6.923$		None		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.h	$867$	$2$	867.i	51.i	$16$	$32$	$4$	$6.923$		None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(16\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.i	$867$	$2$	867.i	51.i	$16$	$32$	$4$	$6.923$		None		$4$	$0$	\(0\)	\(8\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.j	$867$	$2$	867.i	51.i	$16$	$48$	$6$	$6.923$		\(\Q(\sqrt{-3}) \)		$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{U}(1)[D_{16}]$
867.2.i.k	$867$	$2$	867.i	51.i	$16$	$96$	$12$	$6.923$		None		$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$
867.2.i.l	$867$	$2$	867.i	51.i	$16$	$192$	$24$	$6.923$		None		$32$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{16}]$

Decomposition of \(S_{2}^{\mathrm{old}}(867, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(867, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(51, [\chi])\)\(^{\oplus 2}\)