Space of modular forms of level 1960 and weight 2

• Label: 1960.2
• Level: 1960
• Weight: 2
• Dimension: 55279
• Nonzero newspaces: 36
• Sturm bound: 451584
• Trace bound: 12

Defining parameters

Level:	\( N \)	=	\( 1960 = 2^{3} \cdot 5 \cdot 7^{2} \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 36 \)
Sturm bound:			\(451584\)
Trace bound:			\(12\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1960))\).

	Total	New	Old
Modular forms	115776	56443	59333
Cusp forms	110017	55279	54738
Eisenstein series	5759	1164	4595

Trace form

55279 * q - 64 * q^2 - 64 * q^3 - 64 * q^4 - q^5 - 188 * q^6 - 72 * q^7 - 112 * q^8 - 157 * q^9 - 94 * q^10 - 216 * q^11 - 52 * q^12 - 26 * q^13 - 72 * q^14 - 182 * q^15 - 172 * q^16 - 150 * q^17 + 36 * q^18 - 48 * q^19 - 38 * q^20 + 28 * q^22 + 12 * q^23 + 108 * q^24 - 157 * q^25 - 52 * q^26 + 68 * q^27 + 24 * q^28 - 6 * q^29 + 6 * q^30 - 108 * q^31 + 36 * q^32 - 104 * q^33 + 48 * q^34 - 108 * q^35 - 244 * q^36 - 18 * q^37 - 12 * q^38 - 28 * q^39 - 74 * q^40 - 474 * q^41 - 144 * q^42 - 88 * q^43 - 172 * q^44 - 13 * q^45 - 332 * q^46 + 36 * q^47 - 308 * q^48 - 132 * q^49 - 296 * q^50 - 4 * q^51 - 256 * q^52 + 30 * q^53 - 324 * q^54 + 46 * q^55 - 300 * q^56 - 8 * q^57 - 136 * q^58 + 200 * q^59 - 182 * q^60 + 122 * q^61 - 220 * q^62 + 96 * q^63 - 244 * q^64 - 22 * q^65 - 260 * q^66 + 184 * q^67 - 40 * q^68 + 248 * q^69 - 84 * q^70 - 108 * q^71 + 26 * q^73 + 256 * q^74 + 86 * q^75 + 108 * q^76 + 108 * q^77 + 164 * q^78 + 124 * q^79 + 114 * q^80 + 51 * q^81 + 192 * q^82 + 288 * q^83 + 144 * q^84 + 182 * q^85 + 260 * q^86 + 444 * q^87 + 228 * q^88 + 86 * q^89 + 62 * q^90 - 72 * q^91 + 188 * q^92 + 528 * q^93 + 116 * q^94 + 54 * q^95 - 36 * q^96 + 226 * q^97 - 24 * q^98 - 148 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1960))\)

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
1960.2.a	\(\chi_{1960}(1, \cdot)\)	1960.2.a.a	1	1
		1960.2.a.b	1
		1960.2.a.c	1
		1960.2.a.d	1
		1960.2.a.e	1
		1960.2.a.f	1
		1960.2.a.g	1
		1960.2.a.h	1
		1960.2.a.i	1
		1960.2.a.j	1
		1960.2.a.k	1
		1960.2.a.l	1
		1960.2.a.m	1
		1960.2.a.n	1
		1960.2.a.o	1
		1960.2.a.p	2
		1960.2.a.q	2
		1960.2.a.r	2
		1960.2.a.s	2
		1960.2.a.t	2
		1960.2.a.u	2
		1960.2.a.v	3
		1960.2.a.w	3
		1960.2.a.x	4
		1960.2.a.y	4
1960.2.b	\(\chi_{1960}(981, \cdot)\)	n/a	164	1
1960.2.e	\(\chi_{1960}(1959, \cdot)\)	None	0	1
1960.2.g	\(\chi_{1960}(1569, \cdot)\)	1960.2.g.a	2	1
		1960.2.g.b	2
		1960.2.g.c	6
		1960.2.g.d	8
		1960.2.g.e	12
		1960.2.g.f	12
		1960.2.g.g	20
1960.2.h	\(\chi_{1960}(1371, \cdot)\)	n/a	160	1
1960.2.k	\(\chi_{1960}(391, \cdot)\)	None	0	1
1960.2.l	\(\chi_{1960}(589, \cdot)\)	n/a	236	1
1960.2.n	\(\chi_{1960}(979, \cdot)\)	n/a	232	1
1960.2.q	\(\chi_{1960}(361, \cdot)\)	1960.2.q.a	2	2
		1960.2.q.b	2
		1960.2.q.c	2
		1960.2.q.d	2
		1960.2.q.e	2
		1960.2.q.f	2
		1960.2.q.g	2
		1960.2.q.h	2
		1960.2.q.i	2
		1960.2.q.j	2
		1960.2.q.k	2
		1960.2.q.l	2
		1960.2.q.m	2
		1960.2.q.n	2
		1960.2.q.o	2
		1960.2.q.p	4
		1960.2.q.q	4
		1960.2.q.r	4
		1960.2.q.s	4
		1960.2.q.t	4
		1960.2.q.u	4
		1960.2.q.v	4
		1960.2.q.w	6
		1960.2.q.x	8
		1960.2.q.y	8
1960.2.s	\(\chi_{1960}(293, \cdot)\)	n/a	464	2
1960.2.t	\(\chi_{1960}(687, \cdot)\)	None	0	2
1960.2.w	\(\chi_{1960}(883, \cdot)\)	n/a	472	2
1960.2.x	\(\chi_{1960}(97, \cdot)\)	n/a	120	2
1960.2.ba	\(\chi_{1960}(19, \cdot)\)	n/a	464	2
1960.2.bc	\(\chi_{1960}(31, \cdot)\)	None	0	2
1960.2.bf	\(\chi_{1960}(949, \cdot)\)	n/a	464	2
1960.2.bg	\(\chi_{1960}(569, \cdot)\)	n/a	120	2
1960.2.bj	\(\chi_{1960}(411, \cdot)\)	n/a	320	2
1960.2.bl	\(\chi_{1960}(1341, \cdot)\)	n/a	320	2
1960.2.bm	\(\chi_{1960}(999, \cdot)\)	None	0	2
1960.2.bo	\(\chi_{1960}(281, \cdot)\)	n/a	336	6
1960.2.bp	\(\chi_{1960}(313, \cdot)\)	n/a	240	4
1960.2.bs	\(\chi_{1960}(67, \cdot)\)	n/a	928	4
1960.2.bt	\(\chi_{1960}(263, \cdot)\)	None	0	4
1960.2.bw	\(\chi_{1960}(117, \cdot)\)	n/a	928	4
1960.2.by	\(\chi_{1960}(139, \cdot)\)	n/a	1992	6
1960.2.ca	\(\chi_{1960}(29, \cdot)\)	n/a	1992	6
1960.2.cd	\(\chi_{1960}(111, \cdot)\)	None	0	6
1960.2.ce	\(\chi_{1960}(251, \cdot)\)	n/a	1344	6
1960.2.ch	\(\chi_{1960}(169, \cdot)\)	n/a	504	6
1960.2.cj	\(\chi_{1960}(279, \cdot)\)	None	0	6
1960.2.ck	\(\chi_{1960}(141, \cdot)\)	n/a	1344	6
1960.2.cm	\(\chi_{1960}(81, \cdot)\)	n/a	672	12
1960.2.cn	\(\chi_{1960}(43, \cdot)\)	n/a	3984	12
1960.2.cq	\(\chi_{1960}(153, \cdot)\)	n/a	1008	12
1960.2.cr	\(\chi_{1960}(13, \cdot)\)	n/a	3984	12
1960.2.cu	\(\chi_{1960}(127, \cdot)\)	None	0	12
1960.2.cv	\(\chi_{1960}(159, \cdot)\)	None	0	12
1960.2.cy	\(\chi_{1960}(221, \cdot)\)	n/a	2688	12
1960.2.da	\(\chi_{1960}(131, \cdot)\)	n/a	2688	12
1960.2.db	\(\chi_{1960}(9, \cdot)\)	n/a	1008	12
1960.2.de	\(\chi_{1960}(109, \cdot)\)	n/a	3984	12
1960.2.df	\(\chi_{1960}(271, \cdot)\)	None	0	12
1960.2.dj	\(\chi_{1960}(59, \cdot)\)	n/a	3984	12
1960.2.dl	\(\chi_{1960}(23, \cdot)\)	None	0	24
1960.2.dm	\(\chi_{1960}(157, \cdot)\)	n/a	7968	24
1960.2.dp	\(\chi_{1960}(17, \cdot)\)	n/a	2016	24
1960.2.dq	\(\chi_{1960}(107, \cdot)\)	n/a	7968	24

"n/a" means that newforms for that character have not been added to the database yet

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1960))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1960)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(49))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(98))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(196))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(245))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(392))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(490))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(980))\)\(^{\oplus 2}\)