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

• Label: 855.2.bu
• Level: $855$
• Weight: $2$
• Character orbit: 855.bu
• Rep. character: $\chi_{855}(16,\cdot)$
• 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.bu (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 - 6 * q^3 - 6 * q^6 - 36 * q^8 - 18 * q^9 - 6 * q^13 - 6 * q^19 + 18 * q^22 + 36 * q^24 + 24 * q^26 + 6 * q^27 - 24 * q^28 + 18 * q^29 - 24 * q^30 - 36 * q^33 - 18 * q^34 + 78 * q^36 + 6 * q^38 - 24 * q^39 + 42 * q^41 + 72 * q^42 + 48 * q^43 + 30 * q^44 - 36 * q^47 - 108 * q^48 + 480 * q^49 - 12 * q^50 - 24 * q^51 - 24 * q^52 - 48 * q^53 + 96 * q^54 + 6 * q^57 + 84 * q^59 + 84 * q^61 - 72 * q^62 - 24 * q^63 - 222 * q^64 - 48 * q^65 - 24 * q^67 + 84 * q^68 + 18 * q^69 - 48 * q^71 - 102 * q^72 - 150 * q^73 - 168 * q^74 - 96 * q^78 - 6 * q^79 - 102 * q^81 + 18 * q^82 - 48 * q^83 - 108 * q^86 + 120 * q^87 + 36 * q^89 + 84 * q^90 + 48 * q^91 + 336 * q^92 + 174 * q^96 + 54 * q^97 - 132 * q^98 - 60 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
855.2.bu.a	$855$	$2$	855.bu	171.w	$9$	$240$	$40$	$6.827$		None		✓			855.2.bt.a	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$
855.2.bu.b	$855$	$2$	855.bu	171.w	$9$	$240$	$40$	$6.827$		None		✓			855.2.bt.b	$2$	$0$	\(0\)	\(-3\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{9}]$

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

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