Space of modular forms of level 95 and weight 2

• Label: 95.2
• Level: 95
• Weight: 2
• Dimension: 275
• Nonzero newspaces: 9
• Newform subspaces: 18
• Sturm bound: 1440
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 18 \)
Sturm bound:			\(1440\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(95))\).

	Total	New	Old
Modular forms	432	379	53
Cusp forms	289	275	14
Eisenstein series	143	104	39

Trace form

275 * q - 21 * q^2 - 22 * q^3 - 25 * q^4 - 28 * q^5 - 66 * q^6 - 26 * q^7 - 33 * q^8 - 31 * q^9 - 30 * q^10 - 66 * q^11 - 22 * q^12 - 8 * q^13 - 6 * q^14 - 13 * q^15 - 13 * q^16 - 18 * q^17 + 15 * q^18 + 5 * q^19 - 25 * q^20 - 44 * q^21 - 24 * q^23 - 6 * q^24 - 10 * q^25 - 60 * q^26 - 16 * q^27 + 4 * q^28 - 12 * q^29 + 24 * q^30 - 50 * q^31 + 9 * q^32 + 42 * q^33 + 18 * q^34 + q^35 + 71 * q^36 - 2 * q^37 + 51 * q^38 + 16 * q^39 + 39 * q^40 - 60 * q^41 + 66 * q^42 + 16 * q^43 + 42 * q^44 + 41 * q^45 + 36 * q^46 + 24 * q^47 + 110 * q^48 + 3 * q^49 + 69 * q^50 - 18 * q^51 + 16 * q^52 + 24 * q^54 - 3 * q^55 + 60 * q^56 - 4 * q^57 - 54 * q^58 + 12 * q^59 + 98 * q^60 + 16 * q^61 + 84 * q^62 + 46 * q^63 + 131 * q^64 + 58 * q^65 + 90 * q^66 + 100 * q^67 + 108 * q^68 + 84 * q^69 + 93 * q^70 + 39 * q^72 + 76 * q^73 + 48 * q^74 + 2 * q^75 - 7 * q^76 + 30 * q^77 - 42 * q^78 + 34 * q^79 - 112 * q^80 - 85 * q^81 + 54 * q^82 - 84 * q^83 - 242 * q^84 - 81 * q^85 - 132 * q^86 - 138 * q^87 - 234 * q^88 - 54 * q^89 - 219 * q^90 - 142 * q^91 - 240 * q^92 - 230 * q^93 - 252 * q^94 - 91 * q^95 - 504 * q^96 - 98 * q^97 - 135 * q^98 - 192 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(95))\)

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
95.2.a	\(\chi_{95}(1, \cdot)\)	95.2.a.a	3	1
		95.2.a.b	4
95.2.b	\(\chi_{95}(39, \cdot)\)	95.2.b.a	2	1
		95.2.b.b	6
95.2.e	\(\chi_{95}(11, \cdot)\)	95.2.e.a	2	2
		95.2.e.b	6
		95.2.e.c	8
95.2.g	\(\chi_{95}(18, \cdot)\)	95.2.g.a	4	2
		95.2.g.b	12
95.2.i	\(\chi_{95}(49, \cdot)\)	95.2.i.a	4	2
		95.2.i.b	12
95.2.k	\(\chi_{95}(6, \cdot)\)	95.2.k.a	18	6
		95.2.k.b	18
95.2.l	\(\chi_{95}(8, \cdot)\)	95.2.l.a	4	4
		95.2.l.b	4
		95.2.l.c	24
95.2.p	\(\chi_{95}(4, \cdot)\)	95.2.p.a	48	6
95.2.r	\(\chi_{95}(2, \cdot)\)	95.2.r.a	96	12

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)