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

• Label: 115.2.g
• Level: $115$
• Weight: $2$
• Character orbit: 115.g
• Rep. character: $\chi_{115}(6,\cdot)$
• Character field: $\Q(\zeta_{11})$
• Dimension: $80$
• Newform subspaces: $3$
• Sturm bound: $24$
• Trace bound: $1$

Defining parameters

Level:	\( N \)	\(=\)	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	115.g (of order \(11\) and degree \(10\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 23 \)
Character field:			\(\Q(\zeta_{11})\)
Newform subspaces:			\( 3 \)
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	140	80	60
Cusp forms	100	80	20
Eisenstein series	40	0	40

Trace form

80 * q - 4 * q^2 - 16 * q^4 - 2 * q^5 - 14 * q^6 - 4 * q^7 - 18 * q^8 - 12 * q^9 - 6 * q^10 - 16 * q^11 - 6 * q^12 - 4 * q^13 - 12 * q^14 - 4 * q^15 - 4 * q^16 + 6 * q^17 - 42 * q^18 + 6 * q^19 - 6 * q^20 + 22 * q^21 + 16 * q^22 - 18 * q^23 + 96 * q^24 - 8 * q^25 - 10 * q^26 + 30 * q^27 - 48 * q^28 - 24 * q^29 - 8 * q^30 - 8 * q^31 - 16 * q^32 - 48 * q^33 - 22 * q^34 + 16 * q^35 + 8 * q^36 - 40 * q^37 + 22 * q^38 - 20 * q^39 + 58 * q^40 - 6 * q^41 - 104 * q^42 + 56 * q^43 - 30 * q^44 + 40 * q^45 + 104 * q^46 - 64 * q^47 + 86 * q^48 + 8 * q^49 + 18 * q^50 + 20 * q^51 - 66 * q^52 - 28 * q^53 + 12 * q^54 + 28 * q^55 + 80 * q^56 - 14 * q^57 + 68 * q^58 - 4 * q^59 + 10 * q^60 - 12 * q^61 + 70 * q^62 + 18 * q^63 - 62 * q^64 - 24 * q^65 - 92 * q^66 - 32 * q^67 + 112 * q^68 - 96 * q^69 - 12 * q^70 - 66 * q^71 + 18 * q^72 - 4 * q^73 - 38 * q^74 - 24 * q^76 + 90 * q^77 + 158 * q^78 + 40 * q^79 - 30 * q^80 - 60 * q^81 + 78 * q^82 + 86 * q^83 + 134 * q^84 - 18 * q^85 - 102 * q^86 + 152 * q^87 - 16 * q^88 + 28 * q^89 - 42 * q^90 - 68 * q^91 + 42 * q^92 + 148 * q^93 + 32 * q^94 - 16 * q^95 - 162 * q^96 + 56 * q^97 - 12 * q^98 + 104 * 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.g.a	$115$	$2$	115.g	23.c	$11$	$10$	$1$	$0.918$	\(\Q(\zeta_{22})\)	None		✓			115.2.g.a	$2$	$0$	\(5\)	\(1\)	\(1\)	\(5\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(\zeta_{22}+\zeta_{22}^{3}-\zeta_{22}^{4}+\zeta_{22}^{5}+\zeta_{22}^{7}+\cdots)q^{2}+\cdots\)
115.2.g.b	$115$	$2$	115.g	23.c	$11$	$20$	$2$	$0.918$	\(\mathbb{Q}[x]/(x^{20} - \cdots)\)	None		✓			115.2.g.b	$2$	$0$	\(-4\)	\(1\)	\(2\)	\(-4\)	$1$	$\mathrm{SU}(2)[C_{11}]$	\(q+(-1+\beta _{2}+\beta _{3}+\beta _{4}+\beta _{6}+\beta _{8}+\cdots)q^{2}+\cdots\)
115.2.g.c	$115$	$2$	115.g	23.c	$11$	$50$	$5$	$0.918$		None		✓	✓		115.2.g.c	$2$	$0$	\(-5\)	\(-2\)	\(-5\)	\(-5\)		$\mathrm{SU}(2)[C_{11}]$

Decomposition of \(S_{2}^{\mathrm{old}}(115, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(115, [\chi]) \simeq \) \(S_{2}^{\mathrm{new}}(23, [\chi])\)\(^{\oplus 2}\)