Space of modular forms of level 115 and weight 2

• Label: 115.2
• Level: 115
• Weight: 2
• Dimension: 417
• Nonzero newspaces: 6
• Newform subspaces: 11
• Sturm bound: 2112
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 115 = 5 \cdot 23 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 6 \)
Newform subspaces:			\( 11 \)
Sturm bound:			\(2112\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(115))\).

	Total	New	Old
Modular forms	616	545	71
Cusp forms	441	417	24
Eisenstein series	175	128	47

Trace form

417 * q - 25 * q^2 - 26 * q^3 - 29 * q^4 - 34 * q^5 - 78 * q^6 - 30 * q^7 - 37 * q^8 - 35 * q^9 - 36 * q^10 - 78 * q^11 - 50 * q^12 - 36 * q^13 - 46 * q^14 - 26 * q^15 - 53 * q^16 - 18 * q^17 + 27 * q^18 - 20 * q^19 + 4 * q^20 - 32 * q^21 + 8 * q^22 - q^23 + 28 * q^24 - 12 * q^25 - 64 * q^26 + 4 * q^27 + 10 * q^28 - 30 * q^29 - q^30 - 76 * q^31 - 41 * q^32 - 48 * q^33 - 32 * q^34 - 19 * q^35 - 47 * q^36 + 28 * q^37 + 28 * q^38 + 10 * q^39 + 40 * q^40 - 64 * q^41 + 102 * q^42 + 22 * q^43 + 92 * q^44 + 31 * q^45 + 41 * q^46 - 4 * q^47 + 74 * q^48 + 53 * q^49 - 14 * q^50 - 50 * q^51 + 100 * q^52 - 32 * q^53 + 78 * q^54 + 21 * q^55 + 56 * q^56 + 52 * q^57 + 86 * q^58 + 50 * q^59 + 71 * q^60 - 40 * q^61 + 14 * q^62 - 16 * q^63 + 27 * q^64 + 30 * q^65 + 32 * q^66 - 46 * q^67 + 138 * q^68 - 4 * q^69 - 2 * q^70 - 28 * q^71 + 113 * q^72 - 52 * q^73 + 62 * q^74 + 84 * q^75 + 80 * q^76 + 80 * q^77 + 162 * q^78 + 74 * q^79 + 145 * q^80 + 165 * q^81 + 72 * q^82 + 48 * q^83 + 194 * q^84 + 81 * q^85 + 66 * q^86 + 122 * q^87 - 114 * q^88 + 20 * q^89 + 159 * q^90 + 20 * q^91 + 15 * q^92 + 92 * q^93 + 76 * q^94 + 2 * q^95 + 100 * q^96 - 54 * q^97 - 105 * q^98 - 24 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)

We only show spaces with even parity, since no modular forms exist when this condition is not satisfied. Within each space \( S_k^{\mathrm{new}}(N, \chi) \) we list available newforms together with their dimension.

Label	\(\chi\)	Newforms	Dimension	\(\chi\) degree
115.2.a	\(\chi_{115}(1, \cdot)\)	115.2.a.a	1	1
		115.2.a.b	2
		115.2.a.c	4
115.2.b	\(\chi_{115}(24, \cdot)\)	115.2.b.a	2	1
		115.2.b.b	8
115.2.e	\(\chi_{115}(22, \cdot)\)	115.2.e.a	20	2
115.2.g	\(\chi_{115}(6, \cdot)\)	115.2.g.a	10	10
		115.2.g.b	20
		115.2.g.c	50
115.2.j	\(\chi_{115}(4, \cdot)\)	115.2.j.a	100	10
115.2.l	\(\chi_{115}(7, \cdot)\)	115.2.l.a	200	20

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(115))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(115)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 2}\)