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

• Label: 855.2.i
• Level: $855$
• Weight: $2$
• Character orbit: 855.i
• Rep. character: $\chi_{855}(286,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $144$
• Newform subspaces: $4$
• Sturm bound: $240$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.i (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 9 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 4 \)
Sturm bound:			\(240\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

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

	Total	New	Old
Modular forms	248	144	104
Cusp forms	232	144	88
Eisenstein series	16	0	16

Trace form

\( 144 q - 72 q^{4} + 4 q^{5} + 4 q^{6} + 24 q^{8} - 4 q^{9} + O(q^{10}) \)

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.i.a	$855$	$2$	855.i	9.c	$3$	$26$	$13$	$6.827$		None		$2$	$0$	\(3\)	\(-2\)	\(-13\)	\(10\)		$\mathrm{SU}(2)[C_{3}]$
855.2.i.b	$855$	$2$	855.i	9.c	$3$	$30$	$15$	$6.827$		None		$2$	$0$	\(-3\)	\(2\)	\(15\)	\(2\)		$\mathrm{SU}(2)[C_{3}]$
855.2.i.c	$855$	$2$	855.i	9.c	$3$	$42$	$21$	$6.827$		None		$2$	$0$	\(-3\)	\(-2\)	\(-21\)	\(-2\)		$\mathrm{SU}(2)[C_{3}]$
855.2.i.d	$855$	$2$	855.i	9.c	$3$	$46$	$23$	$6.827$		None		$2$	$0$	\(3\)	\(2\)	\(23\)	\(-10\)		$\mathrm{SU}(2)[C_{3}]$

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

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