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 + 2 * q^10 + 4 * q^11 + 4 * q^14 + 10 * q^15 - 4 * q^16 - 8 * q^19 - 16 * q^20 + 24 * q^24 - 10 * q^25 + 20 * q^26 + 2 * q^29 + 14 * q^30 - 10 * q^31 - 8 * q^34 + 26 * q^35 - 12 * q^36 + 8 * q^39 - 10 * q^40 - 30 * q^41 - 12 * q^44 + 20 * q^45 - 4 * q^46 + 12 * q^49 + 12 * q^50 - 28 * q^54 - 16 * q^55 + 28 * q^56 - 6 * q^59 - 24 * q^60 - 28 * q^61 + 56 * q^64 - 10 * q^65 - 16 * q^66 + 8 * q^69 - 36 * q^70 - 22 * q^71 + 44 * q^74 + 16 * q^75 - 4 * q^76 - 20 * q^79 - 18 * q^80 - 6 * q^81 - 12 * q^84 + 22 * q^85 + 44 * q^86 + 44 * q^89 + 56 * q^91 + 92 * q^94 - 36 * q^95 + 28 * q^96 - 72 * q^99

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	Twist minimal	Largest	Maximal	Minimal twist	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		✓			115.2.b.a	$2$	$0$	\(0\)	\(0\)	\(4\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+2 i q^{2}-2 i q^{3}-2 q^{4}+(i+2)q^{5}+\cdots\)
115.2.b.b	$115$	$2$	115.b	5.b	$2$	$8$	$8$	$0.918$	8.0.527896576.2	None		✓	✓		115.2.b.b	$2$	$0$	\(0\)	\(0\)	\(-6\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{2}]$	\(q+\beta _{7}q^{2}+(-\beta _{1}-\beta _{3}+\beta _{5})q^{3}+(-1+\cdots)q^{4}+\cdots\)