Space of modular forms of level 57, weight 2, and Character 57.j

• Label: 57.2.j
• Level: $57$
• Weight: $2$
• Character orbit: 57.j
• Rep. character: $\chi_{57}(2,\cdot)$
• Character field: $\Q(\zeta_{18})$
• Dimension: $30$
• Newform subspaces: $2$
• Sturm bound: $13$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.j (of order \(18\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 57 \)
Character field:			\(\Q(\zeta_{18})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(13\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(57, [\chi])\).

	Total	New	Old
Modular forms	54	54	0
Cusp forms	30	30	0
Eisenstein series	24	24	0

Trace form

\( 30 q - 9 q^{3} - 18 q^{4} - 9 q^{6} - 6 q^{7} + 3 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(57, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
57.2.j.a	$57$	$2$	57.j	57.j	$18$	$6$	$1$	$0.455$	\(\Q(\zeta_{18})\)	\(\Q(\sqrt{-3}) \)		$4$	$0$	\(0\)	\(0\)	\(0\)	\(0\)	$1$	$\mathrm{U}(1)[D_{18}]$	\(q+(-\zeta_{18}^{2}+2\zeta_{18}^{5})q^{3}+2\zeta_{18}q^{4}+\cdots\)
57.2.j.b	$57$	$2$	57.j	57.j	$18$	$24$	$4$	$0.455$		None		$4$	$0$	\(0\)	\(-9\)	\(0\)	\(-6\)		$\mathrm{SU}(2)[C_{18}]$