Space of modular forms of level 115, weight 4, and Character 115.b

• Label: 115.4.b
• Level: $115$
• Weight: $4$
• Character orbit: 115.b
• Rep. character: $\chi_{115}(24,\cdot)$
• Character field: $\Q$
• Dimension: $34$
• Newform subspaces: $1$
• Sturm bound: $48$
• Trace bound: $0$

Defining parameters

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 1 \)
Sturm bound:			\(48\)
Trace bound:			\(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(115, [\chi])\).

	Total	New	Old
Modular forms	38	34	4
Cusp forms	34	34	0
Eisenstein series	4	0	4

Trace form

\( 34 q - 144 q^{4} + 14 q^{5} + 24 q^{6} - 310 q^{9} + O(q^{10}) \)

Decomposition of \(S_{4}^{\mathrm{new}}(115, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
115.4.b.a	$115$	$4$	115.b	5.b	$2$	$34$	$34$	$6.785$		None		$2$	$0$	\(0\)	\(0\)	\(14\)	\(0\)		$\mathrm{SU}(2)[C_{2}]$