Space of modular forms of level 95 and weight 3

• Label: 95.3
• Level: 95
• Weight: 3
• Dimension: 606
• Nonzero newspaces: 9
• Newform subspaces: 12
• Sturm bound: 2160
• Trace bound: 2

Defining parameters

Level:	\( N \)	=	\( 95 = 5 \cdot 19 \)
Weight:	\( k \)	=	\( 3 \)
Nonzero newspaces:			\( 9 \)
Newform subspaces:			\( 12 \)
Sturm bound:			\(2160\)
Trace bound:			\(2\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{3}(\Gamma_1(95))\).

	Total	New	Old
Modular forms	792	706	86
Cusp forms	648	606	42
Eisenstein series	144	100	44

Trace form

606 * q - 18 * q^2 - 18 * q^3 - 18 * q^4 - 27 * q^5 - 54 * q^6 - 18 * q^7 - 18 * q^8 - 18 * q^9 - 27 * q^10 - 54 * q^11 - 162 * q^12 - 138 * q^13 - 162 * q^14 - 81 * q^15 - 198 * q^16 - 36 * q^17 - 36 * q^18 + 24 * q^19 + 18 * q^20 + 72 * q^21 + 198 * q^22 + 72 * q^23 + 414 * q^24 + 99 * q^25 + 234 * q^26 + 18 * q^27 - 264 * q^28 - 306 * q^29 - 468 * q^30 - 270 * q^31 - 468 * q^32 - 450 * q^33 - 288 * q^34 - 99 * q^35 - 306 * q^36 - 36 * q^37 + 108 * q^38 + 180 * q^39 + 198 * q^40 + 90 * q^41 + 882 * q^42 + 336 * q^43 - 36 * q^44 + 108 * q^45 + 36 * q^46 - 144 * q^47 + 360 * q^48 + 120 * q^49 - 108 * q^50 - 252 * q^51 - 546 * q^52 - 234 * q^53 - 396 * q^54 - 63 * q^55 - 72 * q^56 + 72 * q^57 + 108 * q^58 + 252 * q^59 + 216 * q^60 - 534 * q^61 - 540 * q^62 - 666 * q^63 - 546 * q^64 - 162 * q^65 + 90 * q^66 - 708 * q^67 + 612 * q^68 - 180 * q^69 - 63 * q^70 + 468 * q^71 + 324 * q^72 - 240 * q^73 - 234 * q^74 - 36 * q^75 + 126 * q^76 + 630 * q^77 + 1746 * q^78 + 1194 * q^79 + 2745 * q^80 + 1854 * q^81 + 2736 * q^82 + 1152 * q^83 + 4086 * q^84 + 1665 * q^85 + 1908 * q^86 + 2718 * q^87 + 2934 * q^88 + 1764 * q^89 + 1908 * q^90 + 1698 * q^91 + 1800 * q^92 + 1206 * q^93 - 756 * q^95 - 3132 * q^96 - 1332 * q^97 - 3564 * q^98 - 2502 * q^99

Decomposition of \(S_{3}^{\mathrm{new}}(\Gamma_1(95))\)

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
95.3.c	\(\chi_{95}(56, \cdot)\)	95.3.c.a	12	1
95.3.d	\(\chi_{95}(94, \cdot)\)	95.3.d.a	2	1
		95.3.d.b	4
		95.3.d.c	4
		95.3.d.d	8
95.3.f	\(\chi_{95}(58, \cdot)\)	95.3.f.a	36	2
95.3.h	\(\chi_{95}(69, \cdot)\)	95.3.h.a	36	2
95.3.j	\(\chi_{95}(31, \cdot)\)	95.3.j.a	24	2
95.3.m	\(\chi_{95}(7, \cdot)\)	95.3.m.a	72	4
95.3.n	\(\chi_{95}(21, \cdot)\)	95.3.n.a	84	6
95.3.o	\(\chi_{95}(14, \cdot)\)	95.3.o.a	108	6
95.3.q	\(\chi_{95}(17, \cdot)\)	95.3.q.a	216	12

Decomposition of \(S_{3}^{\mathrm{old}}(\Gamma_1(95))\) into lower level spaces

\( S_{3}^{\mathrm{old}}(\Gamma_1(95)) \cong \) \(S_{3}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 4}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 2}\)\(\oplus\)\(S_{3}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 2}\)