Space of modular forms of level 50, weight 6, and Character 50.e

• Label: 50.6.e
• Level: $50$
• Weight: $6$
• Character orbit: 50.e
• Rep. character: $\chi_{50}(9,\cdot)$
• Character field: $\Q(\zeta_{10})$
• Dimension: $48$
• Newform subspaces: $1$
• Sturm bound: $45$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 50 = 2 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	50.e (of order \(10\) and degree \(4\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 25 \)
Character field:			\(\Q(\zeta_{10})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(45\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(50, [\chi])\).

	Total	New	Old
Modular forms	160	48	112
Cusp forms	144	48	96
Eisenstein series	16	0	16

Trace form

\( 48 q + 192 q^{4} + 180 q^{5} + 72 q^{6} + 686 q^{9} + O(q^{10}) \)

Decomposition of \(S_{6}^{\mathrm{new}}(50, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
50.6.e.a	$50$	$6$	50.e	25.e	$10$	$48$	$12$	$8.019$		None		$2$	$0$	\(0\)	\(0\)	\(180\)	\(0\)		$\mathrm{SU}(2)[C_{10}]$

Decomposition of \(S_{6}^{\mathrm{old}}(50, [\chi])\) into lower level spaces

\( S_{6}^{\mathrm{old}}(50, [\chi]) \cong \) \(S_{6}^{\mathrm{new}}(25, [\chi])\)\(^{\oplus 2}\)