Space of modular forms of level 855, weight 2, and Character 855.bt

• Label: 855.2.bt
• Level: $855$
• Weight: $2$
• Character orbit: 855.bt
• Rep. character: $\chi_{855}(61,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $480$
• Newform subspaces: $2$
• Sturm bound: $240$
• Trace bound: $8$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bt (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 171 \)
Character field:			\(\Q(\zeta_{9})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(240\)
Trace bound:			\(8\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(855, [\chi])\).

	Total	New	Old
Modular forms	744	480	264
Cusp forms	696	480	216
Eisenstein series	48	0	48

Trace form

\( 480 q + 12 q^{3} + 12 q^{6} - 36 q^{8} + 36 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(855, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
855.2.bt.a	$855$	$2$	855.bt	171.v	$9$	$240$	$40$	$6.827$		None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
855.2.bt.b	$855$	$2$	855.bt	171.v	$9$	$240$	$40$	$6.827$		None		$2$	$0$	\(0\)	\(6\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

Decomposition of \(S_{2}^{\mathrm{old}}(855, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(855, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(171, [\chi])\)\(^{\oplus 2}\)