Space of modular forms of level 3520 and weight 2

• Label: 3520.2
• Level: 3520
• Weight: 2
• Dimension: 185724
• Nonzero newspaces: 56
• Sturm bound: 1474560
• Trace bound: 97

Defining parameters

Level:	\( N \)	=	\( 3520 = 2^{6} \cdot 5 \cdot 11 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 56 \)
Sturm bound:			\(1474560\)
Trace bound:			\(97\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(3520))\).

	Total	New	Old
Modular forms	374400	188100	186300
Cusp forms	362881	185724	177157
Eisenstein series	11519	2376	9143

Trace form

185724 * q - 128 * q^2 - 96 * q^3 - 128 * q^4 - 192 * q^5 - 384 * q^6 - 104 * q^7 - 128 * q^8 - 172 * q^9 - 192 * q^10 - 332 * q^11 - 288 * q^12 - 160 * q^13 - 128 * q^14 - 156 * q^15 - 384 * q^16 - 256 * q^17 - 128 * q^18 - 128 * q^19 - 192 * q^20 - 368 * q^21 - 128 * q^22 - 224 * q^23 + 32 * q^24 - 208 * q^25 - 224 * q^26 - 72 * q^27 + 32 * q^28 - 64 * q^29 - 32 * q^30 - 200 * q^31 + 32 * q^32 - 56 * q^33 - 128 * q^34 - 140 * q^35 - 64 * q^36 - 96 * q^37 + 32 * q^38 - 88 * q^39 - 112 * q^40 - 480 * q^41 + 32 * q^42 - 144 * q^43 - 128 * q^44 - 440 * q^45 - 384 * q^46 - 168 * q^47 - 128 * q^48 - 260 * q^49 - 240 * q^50 - 184 * q^51 - 320 * q^52 - 224 * q^53 - 384 * q^54 - 100 * q^55 - 1088 * q^56 - 136 * q^57 - 416 * q^58 + 176 * q^59 - 384 * q^60 - 416 * q^61 - 256 * q^62 + 280 * q^63 - 512 * q^64 - 468 * q^65 - 592 * q^66 + 232 * q^67 - 320 * q^68 + 16 * q^69 - 384 * q^70 + 88 * q^71 - 416 * q^72 - 32 * q^73 - 352 * q^74 + 172 * q^75 - 640 * q^76 - 40 * q^77 - 384 * q^78 + 168 * q^79 - 112 * q^80 - 404 * q^81 + 192 * q^82 + 64 * q^83 + 320 * q^84 + 16 * q^85 + 32 * q^86 + 160 * q^87 + 16 * q^88 - 40 * q^89 + 96 * q^90 - 184 * q^91 + 480 * q^92 + 224 * q^93 + 256 * q^94 - 12 * q^95 + 160 * q^96 + 128 * q^97 + 416 * q^98 + 12 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(3520))\)

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
3520.2.a	\(\chi_{3520}(1, \cdot)\)	3520.2.a.a	1	1
		3520.2.a.b	1
		3520.2.a.c	1
		3520.2.a.d	1
		3520.2.a.e	1
		3520.2.a.f	1
		3520.2.a.g	1
		3520.2.a.h	1
		3520.2.a.i	1
		3520.2.a.j	1
		3520.2.a.k	1
		3520.2.a.l	1
		3520.2.a.m	1
		3520.2.a.n	1
		3520.2.a.o	1
		3520.2.a.p	1
		3520.2.a.q	1
		3520.2.a.r	1
		3520.2.a.s	1
		3520.2.a.t	1
		3520.2.a.u	1
		3520.2.a.v	1
		3520.2.a.w	1
		3520.2.a.x	1
		3520.2.a.y	1
		3520.2.a.z	1
		3520.2.a.ba	1
		3520.2.a.bb	1
		3520.2.a.bc	1
		3520.2.a.bd	1
		3520.2.a.be	1
		3520.2.a.bf	1
		3520.2.a.bg	1
		3520.2.a.bh	1
		3520.2.a.bi	2
		3520.2.a.bj	2
		3520.2.a.bk	2
		3520.2.a.bl	2
		3520.2.a.bm	2
		3520.2.a.bn	2
		3520.2.a.bo	2
		3520.2.a.bp	2
		3520.2.a.bq	2
		3520.2.a.br	2
		3520.2.a.bs	2
		3520.2.a.bt	2
		3520.2.a.bu	3
		3520.2.a.bv	3
		3520.2.a.bw	3
		3520.2.a.bx	3
		3520.2.a.by	5
		3520.2.a.bz	5
3520.2.b	\(\chi_{3520}(1409, \cdot)\)	n/a	120	1
3520.2.c	\(\chi_{3520}(1759, \cdot)\)	n/a	144	1
3520.2.f	\(\chi_{3520}(2111, \cdot)\)	3520.2.f.a	2	1
		3520.2.f.b	2
		3520.2.f.c	2
		3520.2.f.d	2
		3520.2.f.e	4
		3520.2.f.f	4
		3520.2.f.g	4
		3520.2.f.h	8
		3520.2.f.i	8
		3520.2.f.j	8
		3520.2.f.k	12
		3520.2.f.l	16
		3520.2.f.m	24
3520.2.g	\(\chi_{3520}(1761, \cdot)\)	3520.2.g.a	2	1
		3520.2.g.b	2
		3520.2.g.c	2
		3520.2.g.d	2
		3520.2.g.e	2
		3520.2.g.f	2
		3520.2.g.g	4
		3520.2.g.h	4
		3520.2.g.i	4
		3520.2.g.j	4
		3520.2.g.k	6
		3520.2.g.l	6
		3520.2.g.m	8
		3520.2.g.n	8
		3520.2.g.o	12
		3520.2.g.p	12
3520.2.l	\(\chi_{3520}(3169, \cdot)\)	n/a	120	1
3520.2.m	\(\chi_{3520}(3519, \cdot)\)	n/a	140	1
3520.2.p	\(\chi_{3520}(351, \cdot)\)	3520.2.p.a	4	1
		3520.2.p.b	4
		3520.2.p.c	12
		3520.2.p.d	12
		3520.2.p.e	32
		3520.2.p.f	32
3520.2.s	\(\chi_{3520}(463, \cdot)\)	n/a	240	2
3520.2.t	\(\chi_{3520}(593, \cdot)\)	n/a	280	2
3520.2.v	\(\chi_{3520}(1231, \cdot)\)	n/a	192	2
3520.2.w	\(\chi_{3520}(881, \cdot)\)	n/a	160	2
3520.2.z	\(\chi_{3520}(287, \cdot)\)	n/a	240	2
3520.2.bb	\(\chi_{3520}(417, \cdot)\)	n/a	288	2
3520.2.bd	\(\chi_{3520}(1473, \cdot)\)	n/a	280	2
3520.2.bf	\(\chi_{3520}(1343, \cdot)\)	n/a	240	2
3520.2.bh	\(\chi_{3520}(529, \cdot)\)	n/a	240	2
3520.2.bi	\(\chi_{3520}(879, \cdot)\)	n/a	280	2
3520.2.bk	\(\chi_{3520}(1167, \cdot)\)	n/a	240	2
3520.2.bl	\(\chi_{3520}(1297, \cdot)\)	n/a	280	2
3520.2.bo	\(\chi_{3520}(641, \cdot)\)	n/a	384	4
3520.2.bp	\(\chi_{3520}(727, \cdot)\)	None	0	4
3520.2.bs	\(\chi_{3520}(153, \cdot)\)	None	0	4
3520.2.bt	\(\chi_{3520}(439, \cdot)\)	None	0	4
3520.2.bv	\(\chi_{3520}(441, \cdot)\)	None	0	4
3520.2.by	\(\chi_{3520}(791, \cdot)\)	None	0	4
3520.2.ca	\(\chi_{3520}(89, \cdot)\)	None	0	4
3520.2.cc	\(\chi_{3520}(857, \cdot)\)	None	0	4
3520.2.cd	\(\chi_{3520}(23, \cdot)\)	None	0	4
3520.2.cf	\(\chi_{3520}(1311, \cdot)\)	n/a	384	4
3520.2.ci	\(\chi_{3520}(959, \cdot)\)	n/a	560	4
3520.2.cj	\(\chi_{3520}(289, \cdot)\)	n/a	576	4
3520.2.co	\(\chi_{3520}(801, \cdot)\)	n/a	384	4
3520.2.cp	\(\chi_{3520}(831, \cdot)\)	n/a	384	4
3520.2.cs	\(\chi_{3520}(479, \cdot)\)	n/a	576	4
3520.2.ct	\(\chi_{3520}(449, \cdot)\)	n/a	560	4
3520.2.cv	\(\chi_{3520}(197, \cdot)\)	n/a	4576	8
3520.2.cx	\(\chi_{3520}(67, \cdot)\)	n/a	3840	8
3520.2.cz	\(\chi_{3520}(309, \cdot)\)	n/a	3840	8
3520.2.da	\(\chi_{3520}(221, \cdot)\)	n/a	2560	8
3520.2.dd	\(\chi_{3520}(219, \cdot)\)	n/a	4576	8
3520.2.de	\(\chi_{3520}(131, \cdot)\)	n/a	3072	8
3520.2.dg	\(\chi_{3520}(373, \cdot)\)	n/a	4576	8
3520.2.di	\(\chi_{3520}(243, \cdot)\)	n/a	3840	8
3520.2.dm	\(\chi_{3520}(17, \cdot)\)	n/a	1120	8
3520.2.dn	\(\chi_{3520}(207, \cdot)\)	n/a	1120	8
3520.2.do	\(\chi_{3520}(79, \cdot)\)	n/a	1120	8
3520.2.dr	\(\chi_{3520}(49, \cdot)\)	n/a	1120	8
3520.2.ds	\(\chi_{3520}(193, \cdot)\)	n/a	1120	8
3520.2.du	\(\chi_{3520}(383, \cdot)\)	n/a	1120	8
3520.2.dw	\(\chi_{3520}(223, \cdot)\)	n/a	1152	8
3520.2.dy	\(\chi_{3520}(673, \cdot)\)	n/a	1152	8
3520.2.ea	\(\chi_{3520}(81, \cdot)\)	n/a	768	8
3520.2.ed	\(\chi_{3520}(271, \cdot)\)	n/a	768	8
3520.2.ee	\(\chi_{3520}(497, \cdot)\)	n/a	1120	8
3520.2.ef	\(\chi_{3520}(47, \cdot)\)	n/a	1120	8
3520.2.ei	\(\chi_{3520}(57, \cdot)\)	None	0	16
3520.2.el	\(\chi_{3520}(487, \cdot)\)	None	0	16
3520.2.em	\(\chi_{3520}(9, \cdot)\)	None	0	16
3520.2.eo	\(\chi_{3520}(151, \cdot)\)	None	0	16
3520.2.er	\(\chi_{3520}(201, \cdot)\)	None	0	16
3520.2.et	\(\chi_{3520}(39, \cdot)\)	None	0	16
3520.2.ev	\(\chi_{3520}(103, \cdot)\)	None	0	16
3520.2.ew	\(\chi_{3520}(457, \cdot)\)	None	0	16
3520.2.ez	\(\chi_{3520}(3, \cdot)\)	n/a	18304	32
3520.2.fb	\(\chi_{3520}(237, \cdot)\)	n/a	18304	32
3520.2.fd	\(\chi_{3520}(51, \cdot)\)	n/a	12288	32
3520.2.fe	\(\chi_{3520}(19, \cdot)\)	n/a	18304	32
3520.2.fh	\(\chi_{3520}(141, \cdot)\)	n/a	12288	32
3520.2.fi	\(\chi_{3520}(69, \cdot)\)	n/a	18304	32
3520.2.fk	\(\chi_{3520}(147, \cdot)\)	n/a	18304	32
3520.2.fm	\(\chi_{3520}(13, \cdot)\)	n/a	18304	32

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(3520))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(3520)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(44))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(88))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(176))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(220))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(352))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(440))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(704))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(880))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1760))\)\(^{\oplus 2}\)