Space of modular forms of level 195 and weight 2

• Label: 195.2
• Level: 195
• Weight: 2
• Dimension: 851
• Nonzero newspaces: 20
• Newform subspaces: 36
• Sturm bound: 5376
• Trace bound: 6

Defining parameters

Level:	\( N \)	=	\( 195 = 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 20 \)
Newform subspaces:			\( 36 \)
Sturm bound:			\(5376\)
Trace bound:			\(6\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(195))\).

	Total	New	Old
Modular forms	1536	979	557
Cusp forms	1153	851	302
Eisenstein series	383	128	255

Trace form

851 * q + 5 * q^2 - 9 * q^3 - 15 * q^4 - q^5 - 35 * q^6 - 24 * q^7 - 27 * q^8 - 17 * q^9 - 61 * q^10 - 4 * q^11 - 59 * q^12 - 57 * q^13 - 24 * q^14 - 27 * q^15 - 119 * q^16 - 22 * q^17 - 55 * q^18 - 92 * q^19 - 57 * q^20 - 80 * q^21 - 116 * q^22 - 24 * q^23 - 63 * q^24 - 49 * q^25 - 83 * q^26 - 93 * q^27 - 136 * q^28 - 26 * q^29 - 41 * q^30 - 88 * q^31 - 47 * q^32 - 20 * q^33 - 62 * q^34 - 16 * q^35 + 33 * q^36 + 22 * q^37 + 68 * q^38 + 31 * q^39 - 111 * q^40 - 62 * q^41 - 24 * q^42 - 116 * q^43 - 44 * q^44 - 7 * q^45 - 240 * q^46 - 64 * q^47 + 41 * q^48 - 129 * q^49 - 85 * q^50 - 74 * q^51 - 67 * q^52 - 22 * q^53 + 37 * q^54 - 4 * q^55 + 48 * q^56 - 12 * q^57 - 22 * q^58 + 44 * q^59 + 173 * q^60 - 138 * q^61 + 120 * q^62 + 112 * q^63 + 149 * q^64 + 117 * q^65 + 140 * q^66 + 84 * q^67 + 310 * q^68 + 168 * q^69 + 144 * q^70 + 136 * q^71 + 297 * q^72 + 94 * q^73 + 154 * q^74 + 113 * q^75 + 140 * q^76 + 96 * q^77 + 281 * q^78 - 16 * q^79 + 63 * q^80 + 79 * q^81 - 58 * q^82 - 12 * q^83 + 88 * q^84 - 112 * q^85 - 52 * q^86 - 34 * q^87 - 228 * q^88 - 138 * q^89 - 43 * q^90 - 264 * q^91 - 168 * q^92 - 104 * q^93 - 296 * q^94 - 156 * q^95 - 211 * q^96 - 194 * q^97 - 155 * q^98 - 148 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)

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
195.2.a	\(\chi_{195}(1, \cdot)\)	195.2.a.a	1	1
		195.2.a.b	1
		195.2.a.c	1
		195.2.a.d	1
		195.2.a.e	3
195.2.b	\(\chi_{195}(181, \cdot)\)	195.2.b.a	2	1
		195.2.b.b	2
		195.2.b.c	4
195.2.c	\(\chi_{195}(79, \cdot)\)	195.2.c.a	2	1
		195.2.c.b	10
195.2.h	\(\chi_{195}(64, \cdot)\)	195.2.h.a	2	1
		195.2.h.b	2
		195.2.h.c	12
195.2.i	\(\chi_{195}(16, \cdot)\)	195.2.i.a	2	2
		195.2.i.b	2
		195.2.i.c	4
		195.2.i.d	6
		195.2.i.e	6
195.2.k	\(\chi_{195}(112, \cdot)\)	195.2.k.a	28	2
195.2.m	\(\chi_{195}(53, \cdot)\)	195.2.m.a	48	2
195.2.n	\(\chi_{195}(44, \cdot)\)	195.2.n.a	48	2
195.2.o	\(\chi_{195}(86, \cdot)\)	195.2.o.a	40	2
195.2.s	\(\chi_{195}(38, \cdot)\)	195.2.s.a	16	2
		195.2.s.b	32
195.2.t	\(\chi_{195}(73, \cdot)\)	195.2.t.a	28	2
195.2.v	\(\chi_{195}(4, \cdot)\)	195.2.v.a	32	2
195.2.ba	\(\chi_{195}(94, \cdot)\)	195.2.ba.a	24	2
195.2.bb	\(\chi_{195}(121, \cdot)\)	195.2.bb.a	4	2
		195.2.bb.b	8
		195.2.bb.c	8
195.2.bd	\(\chi_{195}(67, \cdot)\)	195.2.bd.a	56	4
195.2.bf	\(\chi_{195}(17, \cdot)\)	195.2.bf.a	96	4
195.2.bg	\(\chi_{195}(11, \cdot)\)	195.2.bg.a	72	4
195.2.bh	\(\chi_{195}(59, \cdot)\)	195.2.bh.a	96	4
195.2.bl	\(\chi_{195}(68, \cdot)\)	195.2.bl.a	96	4
195.2.bm	\(\chi_{195}(7, \cdot)\)	195.2.bm.a	56	4

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(195))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(195)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 2}\)