Space of modular forms of level 1520 and weight 2

• Label: 1520.2
• Level: 1520
• Weight: 2
• Dimension: 34982
• Nonzero newspaces: 42
• Sturm bound: 276480
• Trace bound: 14

Defining parameters

Level:	$N$	=	$1520 = 2^{4} \cdot 5 \cdot 19$
Weight:	$k$	=	$2$
Nonzero newspaces:			$42$
Sturm bound:			$276480$
Trace bound:			$14$

Dimensions

The following table gives the dimensions of various subspaces of $M_{2}(\Gamma_1(1520))$.

	Total	New	Old
Modular forms	71136	35902	35234
Cusp forms	67105	34982	32123
Eisenstein series	4031	920	3111

Trace form

34982 * q - 64 * q^2 - 50 * q^3 - 56 * q^4 - 119 * q^5 - 168 * q^6 - 42 * q^7 - 40 * q^8 - 10 * q^9 - 92 * q^10 - 130 * q^11 - 72 * q^12 - 70 * q^13 - 72 * q^14 - 37 * q^15 - 216 * q^16 - 126 * q^17 - 48 * q^18 - 26 * q^19 - 192 * q^20 - 182 * q^21 - 56 * q^22 - 18 * q^23 - 56 * q^24 - 7 * q^25 - 168 * q^26 - 62 * q^27 - 88 * q^28 - 50 * q^29 - 164 * q^30 - 218 * q^31 - 104 * q^32 - 194 * q^33 - 168 * q^34 - 101 * q^35 - 328 * q^36 - 108 * q^37 - 144 * q^38 - 148 * q^39 - 268 * q^40 - 110 * q^41 - 216 * q^42 - 34 * q^43 - 184 * q^44 - 171 * q^45 - 264 * q^46 + 22 * q^47 - 152 * q^48 - 130 * q^49 - 204 * q^50 - 90 * q^51 - 136 * q^52 - 78 * q^53 - 152 * q^54 - 41 * q^55 - 216 * q^56 + 22 * q^57 - 176 * q^58 + 2 * q^59 - 28 * q^60 - 198 * q^61 + 8 * q^62 + 38 * q^63 - 8 * q^64 - 71 * q^65 - 40 * q^66 + 62 * q^67 + 56 * q^68 + 30 * q^69 + 68 * q^70 - 142 * q^71 + 200 * q^72 + 242 * q^73 + 120 * q^74 - 266 * q^75 - 112 * q^76 + 52 * q^77 + 200 * q^78 + 22 * q^79 + 84 * q^80 - 154 * q^81 + 72 * q^82 - 118 * q^83 + 216 * q^84 - 43 * q^85 - 56 * q^86 - 70 * q^87 + 152 * q^88 + 174 * q^89 + 140 * q^90 - 42 * q^91 - 72 * q^92 + 94 * q^93 - 8 * q^94 - 133 * q^95 - 336 * q^96 - 86 * q^97 - 144 * q^98 - 198 * q^99

Decomposition of $S_{2}^{\mathrm{new}}(\Gamma_1(1520))$

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
1520.2.a	$\chi_{1520}(1, \cdot)$	1520.2.a.a	1	1
		1520.2.a.b	1
		1520.2.a.c	1
		1520.2.a.d	1
		1520.2.a.e	1
		1520.2.a.f	1
		1520.2.a.g	1
		1520.2.a.h	1
		1520.2.a.i	1
		1520.2.a.j	1
		1520.2.a.k	2
		1520.2.a.l	2
		1520.2.a.m	2
		1520.2.a.n	2
		1520.2.a.o	2
		1520.2.a.p	3
		1520.2.a.q	3
		1520.2.a.r	3
		1520.2.a.s	3
		1520.2.a.t	4
1520.2.d	$\chi_{1520}(609, \cdot)$	1520.2.d.a	2	1
		1520.2.d.b	2
		1520.2.d.c	4
		1520.2.d.d	4
		1520.2.d.e	4
		1520.2.d.f	4
		1520.2.d.g	4
		1520.2.d.h	6
		1520.2.d.i	6
		1520.2.d.j	6
		1520.2.d.k	12
1520.2.e	$\chi_{1520}(151, \cdot)$	None	0	1
1520.2.f	$\chi_{1520}(761, \cdot)$	None	0	1
1520.2.g	$\chi_{1520}(1519, \cdot)$	1520.2.g.a	2	1
		1520.2.g.b	2
		1520.2.g.c	4
		1520.2.g.d	4
		1520.2.g.e	16
		1520.2.g.f	16
		1520.2.g.g	16
1520.2.j	$\chi_{1520}(911, \cdot)$	1520.2.j.a	2	1
		1520.2.j.b	2
		1520.2.j.c	8
		1520.2.j.d	8
		1520.2.j.e	8
		1520.2.j.f	12
1520.2.k	$\chi_{1520}(1369, \cdot)$	None	0	1
1520.2.p	$\chi_{1520}(759, \cdot)$	None	0	1
1520.2.q	$\chi_{1520}(881, \cdot)$	1520.2.q.a	2	2
		1520.2.q.b	2
		1520.2.q.c	2
		1520.2.q.d	2
		1520.2.q.e	2
		1520.2.q.f	2
		1520.2.q.g	2
		1520.2.q.h	4
		1520.2.q.i	6
		1520.2.q.j	6
		1520.2.q.k	8
		1520.2.q.l	8
		1520.2.q.m	8
		1520.2.q.n	8
		1520.2.q.o	8
		1520.2.q.p	10
1520.2.r	$\chi_{1520}(797, \cdot)$	n/a	472	2
1520.2.t	$\chi_{1520}(1027, \cdot)$	n/a	432	2
1520.2.w	$\chi_{1520}(379, \cdot)$	n/a	472	2
1520.2.y	$\chi_{1520}(381, \cdot)$	n/a	288	2
1520.2.bb	$\chi_{1520}(873, \cdot)$	None	0	2
1520.2.bc	$\chi_{1520}(1103, \cdot)$	n/a	108	2
1520.2.bd	$\chi_{1520}(113, \cdot)$	n/a	116	2
1520.2.be	$\chi_{1520}(343, \cdot)$	None	0	2
1520.2.bi	$\chi_{1520}(229, \cdot)$	n/a	432	2
1520.2.bk	$\chi_{1520}(531, \cdot)$	n/a	320	2
1520.2.bl	$\chi_{1520}(267, \cdot)$	n/a	432	2
1520.2.bn	$\chi_{1520}(37, \cdot)$	n/a	472	2
1520.2.bp	$\chi_{1520}(729, \cdot)$	None	0	2
1520.2.bq	$\chi_{1520}(31, \cdot)$	1520.2.bq.a	2	2
		1520.2.bq.b	2
		1520.2.bq.c	2
		1520.2.bq.d	2
		1520.2.bq.e	2
		1520.2.bq.f	2
		1520.2.bq.g	2
		1520.2.bq.h	2
		1520.2.bq.i	2
		1520.2.bq.j	2
		1520.2.bq.k	4
		1520.2.bq.l	4
		1520.2.bq.m	6
		1520.2.bq.n	6
		1520.2.bq.o	8
		1520.2.bq.p	8
		1520.2.bq.q	12
		1520.2.bq.r	12
1520.2.bv	$\chi_{1520}(1319, \cdot)$	None	0	2
1520.2.by	$\chi_{1520}(711, \cdot)$	None	0	2
1520.2.bz	$\chi_{1520}(49, \cdot)$	n/a	116	2
1520.2.ca	$\chi_{1520}(559, \cdot)$	n/a	120	2
1520.2.cb	$\chi_{1520}(121, \cdot)$	None	0	2
1520.2.ce	$\chi_{1520}(81, \cdot)$	n/a	240	6
1520.2.cf	$\chi_{1520}(597, \cdot)$	n/a	944	4
1520.2.ch	$\chi_{1520}(83, \cdot)$	n/a	944	4
1520.2.ck	$\chi_{1520}(501, \cdot)$	n/a	640	4
1520.2.cm	$\chi_{1520}(179, \cdot)$	n/a	944	4
1520.2.cn	$\chi_{1520}(217, \cdot)$	None	0	4
1520.2.co	$\chi_{1520}(463, \cdot)$	n/a	240	4
1520.2.ct	$\chi_{1520}(673, \cdot)$	n/a	232	4
1520.2.cu	$\chi_{1520}(7, \cdot)$	None	0	4
1520.2.cw	$\chi_{1520}(331, \cdot)$	n/a	640	4
1520.2.cy	$\chi_{1520}(349, \cdot)$	n/a	944	4
1520.2.cz	$\chi_{1520}(387, \cdot)$	n/a	944	4
1520.2.db	$\chi_{1520}(293, \cdot)$	n/a	944	4
1520.2.dd	$\chi_{1520}(279, \cdot)$	None	0	6
1520.2.di	$\chi_{1520}(441, \cdot)$	None	0	6
1520.2.dj	$\chi_{1520}(79, \cdot)$	n/a	360	6
1520.2.dm	$\chi_{1520}(289, \cdot)$	n/a	348	6
1520.2.dn	$\chi_{1520}(71, \cdot)$	None	0	6
1520.2.do	$\chi_{1520}(431, \cdot)$	n/a	240	6
1520.2.dp	$\chi_{1520}(9, \cdot)$	None	0	6
1520.2.ds	$\chi_{1520}(149, \cdot)$	n/a	2832	12
1520.2.dt	$\chi_{1520}(51, \cdot)$	n/a	1920	12
1520.2.dy	$\chi_{1520}(33, \cdot)$	n/a	696	12
1520.2.dz	$\chi_{1520}(23, \cdot)$	None	0	12
1520.2.ec	$\chi_{1520}(187, \cdot)$	n/a	2832	12
1520.2.ed	$\chi_{1520}(13, \cdot)$	n/a	2832	12
1520.2.eg	$\chi_{1520}(53, \cdot)$	n/a	2832	12
1520.2.eh	$\chi_{1520}(43, \cdot)$	n/a	2832	12
1520.2.ek	$\chi_{1520}(393, \cdot)$	None	0	12
1520.2.el	$\chi_{1520}(47, \cdot)$	n/a	720	12
1520.2.em	$\chi_{1520}(61, \cdot)$	n/a	1920	12
1520.2.en	$\chi_{1520}(59, \cdot)$	n/a	2832	12

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

Decomposition of $S_{2}^{\mathrm{old}}(\Gamma_1(1520))$ into lower level spaces

$S_{2}^{\mathrm{old}}(\Gamma_1(1520)) \cong$ $S_{2}^{\mathrm{new}}(\Gamma_1(1))$$^{\oplus 20}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$^{\oplus 16}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$^{\oplus 12}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$^{\oplus 10}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$^{\oplus 8}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$^{\oplus 6}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(95))$$^{\oplus 5}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(190))$$^{\oplus 4}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$^{\oplus 2}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(380))$$^{\oplus 3}$$\oplus$$S_{2}^{\mathrm{new}}(\Gamma_1(760))$$^{\oplus 2}$