Space of modular forms of level 52, weight 4, and Character 52.e

• Label: 52.4.e
• Level: $52$
• Weight: $4$
• Character orbit: 52.e
• Rep. character: $\chi_{52}(9,\cdot)$
• Character field: $\Q(\zeta_{3})$
• Dimension: $6$
• Newform subspaces: $1$
• Sturm bound: $28$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	52.e (of order \(3\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 13 \)
Character field:			\(\Q(\zeta_{3})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(28\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(52, [\chi])\).

	Total	New	Old
Modular forms	48	6	42
Cusp forms	36	6	30
Eisenstein series	12	0	12

Trace form

\( 6 q - 10 q^{5} - 16 q^{7} + 7 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(52, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
52.4.e.a	$52$	$4$	52.e	13.c	$3$	$6$	$3$	$3.068$	6.0.6622206867.2	None		$2$	$0$	\(0\)	\(0\)	\(-10\)	\(-16\)	$2^{2}$	$\mathrm{SU}(2)[C_{3}]$	\(q+(-\beta _{1}-\beta _{5})q^{3}+(-2-\beta _{1}+\beta _{2}+\cdots)q^{5}+\cdots\)

Decomposition of \(S_{4}^{\mathrm{old}}(52, [\chi])\) into lower level spaces

\( S_{4}^{\mathrm{old}}(52, [\chi]) \cong \) \(S_{4}^{\mathrm{new}}(13, [\chi])\)\(^{\oplus 3}\)\(\oplus\)\(S_{4}^{\mathrm{new}}(26, [\chi])\)\(^{\oplus 2}\)