Space of modular forms of level 853, weight 2, and Character 853.e

• Label: 853.2.e
• Level: $853$
• Weight: $2$
• Character orbit: 853.e
• Rep. character: $\chi_{853}(221,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $142$
• Newform subspaces: $2$
• Sturm bound: $142$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 853 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	853.e (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 853 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(142\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(853, [\chi])\).

	Total	New	Old
Modular forms	146	146	0
Cusp forms	142	142	0
Eisenstein series	4	4	0

Trace form

\( 142 q - 3 q^{2} - 6 q^{3} + 71 q^{4} + 136 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(853, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
853.2.e.a	$853$	$2$	853.e	853.e	$6$	$2$	$1$	$6.811$	\(\Q(\sqrt{-3}) \)	None		✓			853.2.e.a	$2$	$1$	\(-3\)	\(-4\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q+(-1-\zeta_{6})q^{2}-2q^{3}+\zeta_{6}q^{4}+(-1+\cdots)q^{5}+\cdots\)
853.2.e.b	$853$	$2$	853.e	853.e	$6$	$140$	$70$	$6.811$		None		✓	✓		853.2.e.b	$2$	$0$	\(0\)	\(-2\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{6}]$