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

• Label: 867.2.t
• Level: $867$
• Weight: $2$
• Character orbit: 867.t
• Rep. character: $\chi_{867}(5,\cdot)$
• Character field: $\Q(\zeta_{272})$
• Dimension: $12800$
• Newform subspaces: $1$
• Sturm bound: $204$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.t (of order \(272\) and degree \(128\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 867 \)
Character field:			\(\Q(\zeta_{272})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(204\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	13312	13312	0
Cusp forms	12800	12800	0
Eisenstein series	512	512	0

Trace form

\( 12800 q - 128 q^{3} - 256 q^{4} - 128 q^{6} - 256 q^{7} - 128 q^{9} + O(q^{10}) \)

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.t.a	$867$	$2$	867.t	867.t	$272$	$12800$	$100$	$6.923$		None		$4$	$0$	\(0\)	\(-128\)	\(0\)	\(-256\)		$\mathrm{SU}(2)[C_{272}]$