Space of modular forms of level 1760 and weight 2

• Label: 1760.2
• Level: 1760
• Weight: 2
• Dimension: 46188
• Nonzero newspaces: 40
• Sturm bound: 368640
• Trace bound: 41

Defining parameters

Level:	\( N \)	=	\( 1760 = 2^{5} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(368640\)
Trace bound:			\(41\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(1760))\).

	Total	New	Old
Modular forms	94720	47268	47452
Cusp forms	89601	46188	43413
Eisenstein series	5119	1080	4039

Trace form

46188 * q - 64 * q^2 - 52 * q^3 - 64 * q^4 - 100 * q^5 - 192 * q^6 - 52 * q^7 - 64 * q^8 - 100 * q^9 - 80 * q^10 - 164 * q^11 - 80 * q^12 - 40 * q^13 - 66 * q^15 - 112 * q^16 - 16 * q^17 + 16 * q^18 - 44 * q^19 - 64 * q^20 - 192 * q^21 - 48 * q^22 - 80 * q^23 - 112 * q^24 - 152 * q^25 - 272 * q^26 + 68 * q^27 - 144 * q^28 - 88 * q^29 - 160 * q^30 - 36 * q^31 - 144 * q^32 - 144 * q^33 - 192 * q^34 + 22 * q^35 - 304 * q^36 + 8 * q^37 - 32 * q^38 + 100 * q^39 - 72 * q^40 - 176 * q^41 + 16 * q^42 + 64 * q^43 + 8 * q^44 - 100 * q^45 - 64 * q^46 + 12 * q^47 + 144 * q^48 + 12 * q^49 - 16 * q^50 - 132 * q^51 - 32 * q^52 + 72 * q^53 - 16 * q^54 - 94 * q^55 - 384 * q^56 - 136 * q^57 - 80 * q^58 - 172 * q^59 - 232 * q^60 - 104 * q^61 - 144 * q^62 - 200 * q^63 - 304 * q^64 - 324 * q^65 - 392 * q^66 - 320 * q^67 - 208 * q^68 - 128 * q^69 - 408 * q^70 - 300 * q^71 - 448 * q^72 - 80 * q^73 - 352 * q^74 - 170 * q^75 - 448 * q^76 + 24 * q^77 - 592 * q^78 + 44 * q^79 - 424 * q^80 - 68 * q^81 - 384 * q^82 + 228 * q^83 - 592 * q^84 - 96 * q^85 - 528 * q^86 + 304 * q^87 - 240 * q^88 - 136 * q^89 - 552 * q^90 + 220 * q^91 - 496 * q^92 + 16 * q^93 - 240 * q^94 + 138 * q^95 - 432 * q^96 + 96 * q^97 - 240 * q^98 + 252 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(1760))\)

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
1760.2.a	\(\chi_{1760}(1, \cdot)\)	1760.2.a.a	1	1
		1760.2.a.b	1
		1760.2.a.c	1
		1760.2.a.d	1
		1760.2.a.e	1
		1760.2.a.f	1
		1760.2.a.g	1
		1760.2.a.h	1
		1760.2.a.i	1
		1760.2.a.j	1
		1760.2.a.k	1
		1760.2.a.l	1
		1760.2.a.m	1
		1760.2.a.n	1
		1760.2.a.o	2
		1760.2.a.p	2
		1760.2.a.q	3
		1760.2.a.r	3
		1760.2.a.s	3
		1760.2.a.t	3
		1760.2.a.u	5
		1760.2.a.v	5
1760.2.b	\(\chi_{1760}(1409, \cdot)\)	1760.2.b.a	2	1
		1760.2.b.b	2
		1760.2.b.c	14
		1760.2.b.d	14
		1760.2.b.e	14
		1760.2.b.f	14
1760.2.c	\(\chi_{1760}(879, \cdot)\)	1760.2.c.a	4	1
		1760.2.c.b	8
		1760.2.c.c	56
1760.2.f	\(\chi_{1760}(351, \cdot)\)	1760.2.f.a	4	1
		1760.2.f.b	4
		1760.2.f.c	16
		1760.2.f.d	24
1760.2.g	\(\chi_{1760}(881, \cdot)\)	1760.2.g.a	4	1
		1760.2.g.b	12
		1760.2.g.c	24
1760.2.l	\(\chi_{1760}(529, \cdot)\)	1760.2.l.a	2	1
		1760.2.l.b	2
		1760.2.l.c	56
1760.2.m	\(\chi_{1760}(1759, \cdot)\)	1760.2.m.a	72	1
1760.2.p	\(\chi_{1760}(1231, \cdot)\)	1760.2.p.a	48	1
1760.2.s	\(\chi_{1760}(727, \cdot)\)	None	0	2
1760.2.t	\(\chi_{1760}(857, \cdot)\)	None	0	2
1760.2.v	\(\chi_{1760}(791, \cdot)\)	None	0	2
1760.2.w	\(\chi_{1760}(441, \cdot)\)	None	0	2
1760.2.z	\(\chi_{1760}(463, \cdot)\)	n/a	120	2
1760.2.bb	\(\chi_{1760}(593, \cdot)\)	n/a	136	2
1760.2.bd	\(\chi_{1760}(417, \cdot)\)	n/a	144	2
1760.2.bf	\(\chi_{1760}(287, \cdot)\)	n/a	120	2
1760.2.bh	\(\chi_{1760}(89, \cdot)\)	None	0	2
1760.2.bi	\(\chi_{1760}(439, \cdot)\)	None	0	2
1760.2.bk	\(\chi_{1760}(23, \cdot)\)	None	0	2
1760.2.bl	\(\chi_{1760}(153, \cdot)\)	None	0	2
1760.2.bo	\(\chi_{1760}(641, \cdot)\)	n/a	192	4
1760.2.bp	\(\chi_{1760}(67, \cdot)\)	n/a	960	4
1760.2.bs	\(\chi_{1760}(373, \cdot)\)	n/a	1136	4
1760.2.bt	\(\chi_{1760}(219, \cdot)\)	n/a	1136	4
1760.2.bv	\(\chi_{1760}(221, \cdot)\)	n/a	640	4
1760.2.by	\(\chi_{1760}(131, \cdot)\)	n/a	768	4
1760.2.ca	\(\chi_{1760}(309, \cdot)\)	n/a	960	4
1760.2.cc	\(\chi_{1760}(197, \cdot)\)	n/a	1136	4
1760.2.cd	\(\chi_{1760}(243, \cdot)\)	n/a	960	4
1760.2.cf	\(\chi_{1760}(271, \cdot)\)	n/a	192	4
1760.2.ci	\(\chi_{1760}(479, \cdot)\)	n/a	288	4
1760.2.cj	\(\chi_{1760}(49, \cdot)\)	n/a	272	4
1760.2.co	\(\chi_{1760}(81, \cdot)\)	n/a	192	4
1760.2.cp	\(\chi_{1760}(831, \cdot)\)	n/a	192	4
1760.2.cs	\(\chi_{1760}(79, \cdot)\)	n/a	272	4
1760.2.ct	\(\chi_{1760}(289, \cdot)\)	n/a	288	4
1760.2.cw	\(\chi_{1760}(457, \cdot)\)	None	0	8
1760.2.cx	\(\chi_{1760}(487, \cdot)\)	None	0	8
1760.2.cy	\(\chi_{1760}(39, \cdot)\)	None	0	8
1760.2.db	\(\chi_{1760}(9, \cdot)\)	None	0	8
1760.2.dc	\(\chi_{1760}(193, \cdot)\)	n/a	576	8
1760.2.de	\(\chi_{1760}(223, \cdot)\)	n/a	576	8
1760.2.dg	\(\chi_{1760}(47, \cdot)\)	n/a	544	8
1760.2.di	\(\chi_{1760}(17, \cdot)\)	n/a	544	8
1760.2.dk	\(\chi_{1760}(201, \cdot)\)	None	0	8
1760.2.dn	\(\chi_{1760}(151, \cdot)\)	None	0	8
1760.2.do	\(\chi_{1760}(57, \cdot)\)	None	0	8
1760.2.dp	\(\chi_{1760}(103, \cdot)\)	None	0	8
1760.2.ds	\(\chi_{1760}(13, \cdot)\)	n/a	4544	16
1760.2.dv	\(\chi_{1760}(3, \cdot)\)	n/a	4544	16
1760.2.dw	\(\chi_{1760}(69, \cdot)\)	n/a	4544	16
1760.2.dy	\(\chi_{1760}(51, \cdot)\)	n/a	3072	16
1760.2.eb	\(\chi_{1760}(141, \cdot)\)	n/a	3072	16
1760.2.ed	\(\chi_{1760}(19, \cdot)\)	n/a	4544	16
1760.2.ef	\(\chi_{1760}(147, \cdot)\)	n/a	4544	16
1760.2.eg	\(\chi_{1760}(237, \cdot)\)	n/a	4544	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(1760))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(1760)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 2}\)