Space of modular forms of level 115, weight 5, and Character 115.i

• Label: 115.5.i
• Level: $115$
• Weight: $5$
• Character orbit: 115.i
• Rep. character: $\chi_{115}(14,\cdot)$
• Character field: $\Q(\zeta_{22})$
• Dimension: $460$
• Newform subspaces: $1$
• Sturm bound: $60$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	115.i (of order \(22\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 115 \)
Character field:			\(\Q(\zeta_{22})\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(60\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(115, [\chi])\).

	Total	New	Old
Modular forms	500	500	0
Cusp forms	460	460	0
Eisenstein series	40	40	0

Trace form

\( 460 q + 306 q^{4} - 11 q^{5} - 182 q^{6} + 944 q^{9} + O(q^{10}) \)

Decomposition of \(S_{5}^{\mathrm{new}}(115, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
115.5.i.a	$115$	$5$	115.i	115.i	$22$	$460$	$46$	$11.888$		None		$4$	$0$	\(0\)	\(0\)	\(-11\)	\(0\)		$\mathrm{SU}(2)[C_{22}]$