Space of modular forms of level 53, weight 2, and Character 53.e

• Label: 53.2.e
• Level: $53$
• Weight: $2$
• Character orbit: 53.e
• Rep. character: $\chi_{53}(4,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $9$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 53 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	53.e (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 53 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(9\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(53, [\chi])\).

	Total	New	Old
Modular forms	72	72	0
Cusp forms	48	48	0
Eisenstein series	24	24	0

Trace form

\( 48 q - 13 q^{2} - 13 q^{3} - 9 q^{4} - 13 q^{5} - 17 q^{6} - 5 q^{7} + 13 q^{8} - 5 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(53, [\chi])\) 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
																		$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
53.2.e.a	$53$	$2$	53.e	53.e	$26$	$48$	$4$	$0.423$		None		✓	✓	✓	53.2.e.a	$2$	$0$	\(-13\)	\(-13\)	\(-13\)	\(-5\)		$\mathrm{SU}(2)[C_{26}]$