Space of modular forms of level 158, weight 5, and Character 158.f

• Label: 158.5.f
• Level: $158$
• Weight: $5$
• Character orbit: 158.f
• Rep. character: $\chi_{158}(15,\cdot)$
• Character field: $\Q(\zeta_{26})$
• Dimension: $336$
• Newform subspaces: $1$
• Sturm bound: $100$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 158 = 2 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	158.f (of order \(26\) and degree \(12\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 79 \)
Character field:			\(\Q(\zeta_{26})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(100\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(158, [\chi])\).

	Total	New	Old
Modular forms	984	336	648
Cusp forms	936	336	600
Eisenstein series	48	0	48

Trace form

\( 336 q - 224 q^{4} + 728 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(158, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Twist minimal	Minimal twist	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
																$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
158.5.f.a	$158$	$5$	158.f	79.f	$26$	$336$	$28$	$16.332$		None		✓	158.5.f.a	$2$	$0$	\(0\)	\(0\)	\(0\)	\(0\)		$\mathrm{SU}(2)[C_{26}]$

Decomposition of \(S_{5}^{\mathrm{old}}(158, [\chi])\) into lower level spaces

\( S_{5}^{\mathrm{old}}(158, [\chi]) \simeq \) \(S_{5}^{\mathrm{new}}(79, [\chi])\)\(^{\oplus 2}\)