Space of modular forms of level 95 and weight 5

• Label: 95.5
• Level: 95
• Weight: 5
• Dimension: 1262
• Nonzero newspaces: 9
• Newform subspaces: 13
• Sturm bound: 3600
• Trace bound: 1

Defining parameters

Level:	\( N \)	=	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	=	\( 5 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 13 \)
Sturm bound:			\(3600\)
Trace bound:			\(1\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{5}(\Gamma_1(95))\).

	Total	New	Old
Modular forms	1512	1362	150
Cusp forms	1368	1262	106
Eisenstein series	144	100	44

Trace form

1262 * q - 14 * q^2 + 6 * q^3 - 18 * q^4 - 107 * q^5 - 102 * q^6 + 86 * q^7 + 102 * q^8 - 18 * q^9 - 7 * q^10 - 22 * q^11 - 2082 * q^12 - 454 * q^13 + 1710 * q^14 + 1947 * q^15 + 4634 * q^16 + 580 * q^17 - 72 * q^18 - 1572 * q^19 - 3486 * q^20 - 5460 * q^21 - 6098 * q^22 - 1244 * q^23 - 5202 * q^24 - 853 * q^25 + 4514 * q^26 - 306 * q^27 - 152 * q^28 - 1746 * q^29 + 3864 * q^30 + 3274 * q^31 + 14956 * q^32 + 21390 * q^33 + 15912 * q^34 + 5245 * q^35 + 11934 * q^36 + 968 * q^37 - 9828 * q^38 - 16020 * q^39 - 9102 * q^40 - 2806 * q^41 - 51870 * q^42 - 33988 * q^43 - 60876 * q^44 - 19926 * q^45 - 16052 * q^46 - 1436 * q^47 + 62952 * q^48 + 34260 * q^49 + 50140 * q^50 + 58236 * q^51 + 54230 * q^52 + 34258 * q^53 + 20988 * q^54 + 4537 * q^55 - 6312 * q^56 - 8028 * q^57 - 14244 * q^58 - 29448 * q^59 - 74256 * q^60 - 103502 * q^61 - 107404 * q^62 - 60498 * q^63 - 56514 * q^64 - 23132 * q^65 + 20346 * q^66 + 71120 * q^67 + 88868 * q^68 + 109872 * q^69 + 93417 * q^70 + 127736 * q^71 + 211788 * q^72 + 63740 * q^73 + 20862 * q^74 + 18564 * q^75 - 32274 * q^76 - 13558 * q^77 + 29418 * q^78 - 59262 * q^79 + 48445 * q^80 - 138978 * q^81 - 241400 * q^82 - 108116 * q^83 - 316026 * q^84 - 136915 * q^85 - 121156 * q^86 - 189378 * q^87 - 165282 * q^88 - 14112 * q^89 - 135432 * q^90 + 105154 * q^91 + 99496 * q^92 + 136110 * q^93 - 66150 * q^95 - 98364 * q^96 - 15268 * q^97 + 21728 * q^98 + 128070 * q^99

Decomposition of \(S_{5}^{\mathrm{new}}(\Gamma_1(95))\)

We only show spaces with odd 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
95.5.c	\(\chi_{95}(56, \cdot)\)	95.5.c.a	28	1
95.5.d	\(\chi_{95}(94, \cdot)\)	95.5.d.a	2	1
		95.5.d.b	2
		95.5.d.c	2
		95.5.d.d	4
		95.5.d.e	28
95.5.f	\(\chi_{95}(58, \cdot)\)	95.5.f.a	72	2
95.5.h	\(\chi_{95}(69, \cdot)\)	95.5.h.a	76	2
95.5.j	\(\chi_{95}(31, \cdot)\)	95.5.j.a	56	2
95.5.m	\(\chi_{95}(7, \cdot)\)	95.5.m.a	152	4
95.5.n	\(\chi_{95}(21, \cdot)\)	95.5.n.a	156	6
95.5.o	\(\chi_{95}(14, \cdot)\)	95.5.o.a	228	6
95.5.q	\(\chi_{95}(17, \cdot)\)	95.5.q.a	456	12

Decomposition of \(S_{5}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

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