Space of modular forms of level 80, weight 4, and Character 80.s

• Label: 80.4.s
• Level: $80$
• Weight: $4$
• Character orbit: 80.s
• Rep. character: $\chi_{80}(3,\cdot)$
• Character field: $\Q(\zeta_{4})$
• Dimension: $68$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 80 = 2^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	80.s (of order \(4\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 80 \)
Character field:			\(\Q(i)\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(80, [\chi])\).

	Total	New	Old
Modular forms	76	76	0
Cusp forms	68	68	0
Eisenstein series	8	8	0

Trace form

\( 68 q - 2 q^{2} - 4 q^{3} - 12 q^{4} - 2 q^{5} - 4 q^{6} - 4 q^{7} + 40 q^{8} + 540 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(80, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
80.4.s.a	$80$	$4$	80.s	80.s	$4$	$68$	$34$	$4.720$		None		$2$	$0$	\(-2\)	\(-4\)	\(-2\)	\(-4\)		$\mathrm{SU}(2)[C_{4}]$