Space of modular forms of level 57, weight 5, and Character 57.c

• Label: 57.5.c
• Level: $57$
• Weight: $5$
• Character orbit: 57.c
• Rep. character: $\chi_{57}(37,\cdot)$
• Character field: $\Q$
• Dimension: $14$
• Newform subspaces: $1$
• Sturm bound: $33$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	57.c (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 19 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(33\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(57, [\chi])\).

	Total	New	Old
Modular forms	28	14	14
Cusp forms	24	14	10
Eisenstein series	4	0	4

Trace form

\( 14 q - 156 q^{4} + 18 q^{5} + 36 q^{6} - 54 q^{7} - 378 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(57, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
57.5.c.a	$57$	$5$	57.c	19.b	$2$	$14$	$14$	$5.892$	\(\mathbb{Q}[x]/(x^{14} + \cdots)\)	None		$2$	$0$	\(0\)	\(0\)	\(18\)	\(-54\)	$2^{11}\cdot 3^{4}$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{1}q^{2}-\beta _{5}q^{3}+(-11+\beta _{2})q^{4}+\cdots\)

Decomposition of \(S_{5}^{\mathrm{old}}(57, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(57, [\chi]) \cong \) \(S_{5}^{\mathrm{new}}(19, [\chi])\)\(^{\oplus 2}\)