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

• Label: 57.2.i
• Level: $57$
• Weight: $2$
• Character orbit: 57.i
• Rep. character: $\chi_{57}(4,\cdot)$
• Character field: $\Q(\zeta_{9})$
• Dimension: $18$
• Newform subspaces: $2$
• Sturm bound: $13$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.i (of order \(9\) and degree \(6\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q(\zeta_{9})\)
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	18	36
Cusp forms	30	18	12
Eisenstein series	24	0	24

Trace form

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

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	Twist minimal	Largest	Maximal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
57.2.i.a	$57$	$2$	57.i	19.e	$9$	$6$	$1$	$0.455$	\(\Q(\zeta_{18})\)	None		✓			57.2.i.a	$2$	$0$	\(3\)	\(0\)	\(-6\)	\(3\)	$1$	$\mathrm{SU}(2)[C_{9}]$	\(q+(\zeta_{18}^{2}+\zeta_{18}^{3}-\zeta_{18}^{5})q^{2}-\zeta_{18}^{4}q^{3}+\cdots\)
57.2.i.b	$57$	$2$	57.i	19.e	$9$	$12$	$2$	$0.455$	\(\mathbb{Q}[x]/(x^{12} - \cdots)\)	None		✓	✓		57.2.i.b	$2$	$0$	\(-3\)	\(0\)	\(6\)	\(-9\)	$3$	$\mathrm{SU}(2)[C_{9}]$	\(q+(1-\beta _{1}-\beta _{2}+\beta _{5}-\beta _{9})q^{2}-\beta _{6}q^{3}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(57, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(57, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)