Space of modular forms of level 115, weight 2, and Character 115.b

• Label: 115.2.b
• Level: $115$
• Weight: $2$
• Character orbit: 115.b
• Rep. character: $\chi_{115}(24,\cdot)$
• Character field: $\Q$
• Dimension: $10$
• Newform subspaces: $2$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.b (of order \(2\) and degree \(1\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 5 \)
Character field:			\(\Q\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(24\)
Trace bound:			\(1\)
Distinguishing \(T_p\):			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(115, [\chi])\).

	Total	New	Old
Modular forms	14	10	4
Cusp forms	10	10	0
Eisenstein series	4	0	4

Trace form

\( 10 q - 8 q^{4} - 2 q^{5} - 4 q^{6} - 10 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(115, [\chi])\) 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
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
115.2.b.a	$115$	$2$	115.b	5.b	$2$	$2$	$2$	$0.918$	\(\Q(\sqrt{-1}) \)	None		$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2iq^{2}-2iq^{3}-2q^{4}+(2+i)q^{5}+\cdots\)
115.2.b.b	$115$	$2$	115.b	5.b	$2$	$8$	$8$	$0.918$	8.0.527896576.2	None		$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)