Space of modular forms of level 95 and weight 4

• Label: 95.4
• Level: 95
• Weight: 4
• Dimension: 934
• Nonzero newspaces: 9
• Newform subspaces: 20
• Sturm bound: 2880
• Trace bound: 4

Defining parameters

Level:	\( N \)	=	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	=	\( 4 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 20 \)
Sturm bound:			\(2880\)
Trace bound:			\(4\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{4}(\Gamma_1(95))\).

	Total	New	Old
Modular forms	1152	1038	114
Cusp forms	1008	934	74
Eisenstein series	144	104	40

Trace form

934 * q - 10 * q^2 - 22 * q^3 - 34 * q^4 - 17 * q^5 - 38 * q^6 - 30 * q^7 - 18 * q^8 + 28 * q^9 - 67 * q^10 - 118 * q^11 + 526 * q^12 + 346 * q^13 + 102 * q^14 - 115 * q^15 - 790 * q^16 - 358 * q^17 - 1156 * q^18 - 874 * q^19 - 550 * q^20 - 582 * q^21 - 86 * q^22 + 174 * q^23 + 846 * q^24 + 355 * q^25 + 1010 * q^26 + 2792 * q^27 + 4476 * q^28 + 1342 * q^29 + 1090 * q^30 + 342 * q^31 - 1160 * q^32 - 1982 * q^33 - 2060 * q^34 - 1083 * q^35 - 5842 * q^36 - 1864 * q^37 - 4280 * q^38 - 3664 * q^39 - 1908 * q^40 - 998 * q^41 - 2982 * q^42 - 650 * q^43 + 5320 * q^44 + 2821 * q^45 + 6360 * q^46 + 4754 * q^47 + 11452 * q^48 + 4016 * q^49 + 2378 * q^50 + 112 * q^51 - 4162 * q^52 - 3190 * q^53 - 5732 * q^54 - 1651 * q^55 - 12132 * q^56 - 5258 * q^57 - 4324 * q^58 - 5518 * q^59 - 1406 * q^60 + 6490 * q^61 + 5940 * q^62 + 7026 * q^63 + 9214 * q^64 + 2203 * q^65 + 7514 * q^66 + 1566 * q^67 + 6748 * q^68 + 942 * q^69 - 591 * q^70 + 3478 * q^71 - 8244 * q^72 - 8144 * q^73 - 8258 * q^74 - 1918 * q^75 - 14354 * q^76 - 17376 * q^77 - 25718 * q^78 - 17058 * q^79 - 22843 * q^80 - 14522 * q^81 - 13216 * q^82 - 4002 * q^83 - 4314 * q^84 + 1745 * q^85 + 9476 * q^86 + 13862 * q^87 + 21006 * q^88 + 15294 * q^89 + 31718 * q^90 + 22146 * q^91 + 31632 * q^92 + 27522 * q^93 + 28612 * q^94 + 16331 * q^95 + 53156 * q^96 + 15410 * q^97 + 34480 * q^98 + 24332 * q^99

Decomposition of \(S_{4}^{\mathrm{new}}(\Gamma_1(95))\)

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
95.4.a	\(\chi_{95}(1, \cdot)\)	95.4.a.a	1	1
		95.4.a.b	1
		95.4.a.c	1
		95.4.a.d	1
		95.4.a.e	3
		95.4.a.f	5
		95.4.a.g	6
95.4.b	\(\chi_{95}(39, \cdot)\)	95.4.b.a	12	1
		95.4.b.b	16
95.4.e	\(\chi_{95}(11, \cdot)\)	95.4.e.a	2	2
		95.4.e.b	18
		95.4.e.c	20
95.4.g	\(\chi_{95}(18, \cdot)\)	95.4.g.a	4	2
		95.4.g.b	52
95.4.i	\(\chi_{95}(49, \cdot)\)	95.4.i.a	56	2
95.4.k	\(\chi_{95}(6, \cdot)\)	95.4.k.a	60	6
		95.4.k.b	60
95.4.l	\(\chi_{95}(8, \cdot)\)	95.4.l.a	112	4
95.4.p	\(\chi_{95}(4, \cdot)\)	95.4.p.a	168	6
95.4.r	\(\chi_{95}(2, \cdot)\)	95.4.r.a	336	12

Decomposition of \(S_{4}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

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