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

• Label: 855.2.bx
• Level: $855$
• Weight: $2$
• Character orbit: 855.bx
• Rep. character: $\chi_{855}(68,\cdot)$
• Character field: $\Q(\zeta_{12})$
• Dimension: $464$
• Newform subspaces: $1$
• Sturm bound: $240$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.bx (of order \(12\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 855 \)
Character field:			\(\Q(\zeta_{12})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(240\)
Trace bound:			\(0\)

Dimensions

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

	Total	New	Old
Modular forms	496	496	0
Cusp forms	464	464	0
Eisenstein series	32	32	0

Trace form

464 * q - 2 * q^3 - 6 * q^5 - 4 * q^6 - 4 * q^7 - 4 * q^10 - 24 * q^11 + 2 * q^12 - 4 * q^13 - 8 * q^15 - 424 * q^16 - 18 * q^17 - 24 * q^18 - 12 * q^20 - 4 * q^21 + 10 * q^22 + 2 * q^25 - 2 * q^27 - 20 * q^28 + 2 * q^30 - 8 * q^31 - 8 * q^33 + 76 * q^36 - 16 * q^37 - 18 * q^38 + 18 * q^40 + 36 * q^41 + 82 * q^42 - 4 * q^43 + 6 * q^45 - 56 * q^46 + 54 * q^47 - 36 * q^48 - 108 * q^50 + 12 * q^51 + 68 * q^52 - 14 * q^55 - 24 * q^56 - 6 * q^57 - 12 * q^58 + 78 * q^60 + 4 * q^61 + 12 * q^62 - 70 * q^63 - 84 * q^65 - 4 * q^66 - 4 * q^67 - 60 * q^68 + 42 * q^70 + 14 * q^72 - 4 * q^73 + 98 * q^75 + 24 * q^76 - 12 * q^77 - 64 * q^78 - 120 * q^80 - 36 * q^81 + 4 * q^82 - 12 * q^83 - 4 * q^85 + 102 * q^87 + 48 * q^88 - 46 * q^90 - 8 * q^91 - 22 * q^93 + 54 * q^95 + 96 * q^96 - 4 * q^97 - 42 * q^98

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.bx.a	$855$	$2$	855.bx	855.ax	$12$	$464$	$116$	$6.827$		None		✓	✓	✓	855.2.bx.a	$4$	$0$	\(0\)	\(-2\)	\(-6\)	\(-4\)		$\mathrm{SU}(2)[C_{12}]$