Space of modular forms of level 855, weight 1, and Character 855.u

• Label: 855.1.u
• Level: $855$
• Weight: $1$
• Character orbit: 855.u
• Rep. character: $\chi_{855}(539,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $8$
• Newform subspaces: $1$
• Sturm bound: $120$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 1 \)
Character orbit:	\([\chi]\)	\(=\)	855.u (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 285 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(120\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{1}(855, [\chi])\).

	Total	New	Old
Modular forms	32	8	24
Cusp forms	16	8	8
Eisenstein series	16	0	16

The following table gives the dimensions of subspaces with specified projective image type.

	\(D_n\)	\(A_4\)	\(S_4\)	\(A_5\)
Dimension	0	0	8	0

Trace form

\( 8 q - 4 q^{4} - 4 q^{10} + 4 q^{16} - 8 q^{19} - 8 q^{31} + 8 q^{34} - 4 q^{55} + 4 q^{61} - 8 q^{64} - 4 q^{70} + 4 q^{76} + 4 q^{79} + 4 q^{85} + 4 q^{91}+O(q^{100}) \)

Decomposition of \(S_{1}^{\mathrm{new}}(855, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	Image	CM	RM	Self-dual	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																				$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
855.1.u.a	$855$	$1$	855.u	285.n	$6$	$8$	$4$	$0.427$	\(\Q(\zeta_{24})\)	$S_{4}$	None	None		✓	✓	✓	855.1.u.a	$8$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$		\(q+(-\zeta_{24}^{5}-\zeta_{24}^{11})q^{2}-\zeta_{24}^{4}q^{4}+\cdots\)

Decomposition of \(S_{1}^{\mathrm{old}}(855, [\chi])\) into lower level spaces

\( S_{1}^{\mathrm{old}}(855, [\chi]) \simeq \) \(S_{1}^{\mathrm{new}}(285, [\chi])\)\(^{\oplus 2}\)