Space of modular forms of level 2520 and weight 2

• Label: 2520.2
• Level: 2520
• Weight: 2
• Dimension: 64354
• Nonzero newspaces: 90
• Sturm bound: 663552
• Trace bound: 40

Defining parameters

Level:	\( N \)	=	\( 2520 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 90 \)
Sturm bound:			\(663552\)
Trace bound:			\(40\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2520))\).

	Total	New	Old
Modular forms	170496	65434	105062
Cusp forms	161281	64354	96927
Eisenstein series	9215	1080	8135

Trace form

64354 * q - 20 * q^2 - 28 * q^3 - 20 * q^4 + 10 * q^5 - 112 * q^6 - 24 * q^7 - 104 * q^8 - 68 * q^9 - 138 * q^10 - 108 * q^11 - 72 * q^12 + 8 * q^13 - 64 * q^14 - 160 * q^15 - 132 * q^16 - 96 * q^17 - 16 * q^18 - 156 * q^19 - 68 * q^20 - 32 * q^21 - 92 * q^22 - 192 * q^23 + 80 * q^24 - 128 * q^25 - 40 * q^26 - 64 * q^27 - 148 * q^28 - 60 * q^29 + 52 * q^30 - 288 * q^31 + 120 * q^32 - 156 * q^33 - 76 * q^34 - 138 * q^35 - 24 * q^36 - 136 * q^37 + 208 * q^38 + 24 * q^39 + 40 * q^40 - 312 * q^41 + 92 * q^42 - 92 * q^43 + 356 * q^44 - 44 * q^45 + 56 * q^46 + 16 * q^47 + 176 * q^48 - 206 * q^49 + 244 * q^50 - 20 * q^51 + 264 * q^52 - 80 * q^53 + 192 * q^54 - 72 * q^55 + 104 * q^56 - 148 * q^57 + 296 * q^58 + 144 * q^59 + 104 * q^60 - 60 * q^61 + 200 * q^62 + 104 * q^63 + 172 * q^64 - 52 * q^65 - 128 * q^66 + 28 * q^67 + 260 * q^68 + 208 * q^69 + 236 * q^70 + 256 * q^71 - 168 * q^73 + 308 * q^74 + 280 * q^75 + 284 * q^76 + 252 * q^77 + 40 * q^78 + 248 * q^79 + 320 * q^80 + 84 * q^81 + 540 * q^82 + 668 * q^83 + 304 * q^84 - 4 * q^85 + 356 * q^86 + 480 * q^87 + 468 * q^88 + 248 * q^89 + 160 * q^90 + 132 * q^91 + 580 * q^92 + 296 * q^93 + 516 * q^94 + 576 * q^95 + 448 * q^96 + 32 * q^97 + 548 * q^98 + 504 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2520))\)

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
2520.2.a	\(\chi_{2520}(1, \cdot)\)	2520.2.a.a	1	1
		2520.2.a.b	1
		2520.2.a.c	1
		2520.2.a.d	1
		2520.2.a.e	1
		2520.2.a.f	1
		2520.2.a.g	1
		2520.2.a.h	1
		2520.2.a.i	1
		2520.2.a.j	1
		2520.2.a.k	1
		2520.2.a.l	1
		2520.2.a.m	1
		2520.2.a.n	1
		2520.2.a.o	1
		2520.2.a.p	1
		2520.2.a.q	1
		2520.2.a.r	1
		2520.2.a.s	1
		2520.2.a.t	1
		2520.2.a.u	2
		2520.2.a.v	2
		2520.2.a.w	2
		2520.2.a.x	2
		2520.2.a.y	2
2520.2.d	\(\chi_{2520}(2071, \cdot)\)	None	0	1
2520.2.e	\(\chi_{2520}(1331, \cdot)\)	2520.2.e.a	48	1
		2520.2.e.b	48
2520.2.f	\(\chi_{2520}(881, \cdot)\)	2520.2.f.a	8	1
		2520.2.f.b	8
		2520.2.f.c	8
		2520.2.f.d	8
2520.2.g	\(\chi_{2520}(1261, \cdot)\)	n/a	120	1
2520.2.j	\(\chi_{2520}(2269, \cdot)\)	n/a	180	1
2520.2.k	\(\chi_{2520}(1889, \cdot)\)	2520.2.k.a	24	1
		2520.2.k.b	24
2520.2.p	\(\chi_{2520}(2339, \cdot)\)	n/a	144	1
2520.2.q	\(\chi_{2520}(559, \cdot)\)	None	0	1
2520.2.t	\(\chi_{2520}(1009, \cdot)\)	2520.2.t.a	2	1
		2520.2.t.b	2
		2520.2.t.c	2
		2520.2.t.d	2
		2520.2.t.e	2
		2520.2.t.f	4
		2520.2.t.g	6
		2520.2.t.h	6
		2520.2.t.i	6
		2520.2.t.j	6
		2520.2.t.k	6
2520.2.u	\(\chi_{2520}(629, \cdot)\)	n/a	192	1
2520.2.v	\(\chi_{2520}(1079, \cdot)\)	None	0	1
2520.2.w	\(\chi_{2520}(1819, \cdot)\)	n/a	236	1
2520.2.z	\(\chi_{2520}(811, \cdot)\)	n/a	160	1
2520.2.ba	\(\chi_{2520}(71, \cdot)\)	None	0	1
2520.2.bf	\(\chi_{2520}(2141, \cdot)\)	n/a	128	1
2520.2.bg	\(\chi_{2520}(121, \cdot)\)	n/a	192	2
2520.2.bh	\(\chi_{2520}(841, \cdot)\)	n/a	144	2
2520.2.bi	\(\chi_{2520}(361, \cdot)\)	2520.2.bi.a	2	2
		2520.2.bi.b	2
		2520.2.bi.c	2
		2520.2.bi.d	2
		2520.2.bi.e	2
		2520.2.bi.f	2
		2520.2.bi.g	2
		2520.2.bi.h	2
		2520.2.bi.i	2
		2520.2.bi.j	4
		2520.2.bi.k	4
		2520.2.bi.l	4
		2520.2.bi.m	6
		2520.2.bi.n	6
		2520.2.bi.o	6
		2520.2.bi.p	6
		2520.2.bi.q	6
		2520.2.bi.r	10
		2520.2.bi.s	10
2520.2.bj	\(\chi_{2520}(961, \cdot)\)	n/a	192	2
2520.2.bm	\(\chi_{2520}(1693, \cdot)\)	n/a	472	2
2520.2.bn	\(\chi_{2520}(953, \cdot)\)	2520.2.bn.a	16	2
		2520.2.bn.b	16
		2520.2.bn.c	20
		2520.2.bn.d	20
2520.2.bo	\(\chi_{2520}(127, \cdot)\)	None	0	2
2520.2.bp	\(\chi_{2520}(1763, \cdot)\)	n/a	384	2
2520.2.bu	\(\chi_{2520}(883, \cdot)\)	n/a	360	2
2520.2.bv	\(\chi_{2520}(503, \cdot)\)	None	0	2
2520.2.bw	\(\chi_{2520}(433, \cdot)\)	n/a	120	2
2520.2.bx	\(\chi_{2520}(197, \cdot)\)	n/a	288	2
2520.2.ca	\(\chi_{2520}(1859, \cdot)\)	n/a	1136	2
2520.2.cb	\(\chi_{2520}(439, \cdot)\)	None	0	2
2520.2.cg	\(\chi_{2520}(709, \cdot)\)	n/a	1136	2
2520.2.ch	\(\chi_{2520}(689, \cdot)\)	n/a	288	2
2520.2.ck	\(\chi_{2520}(2201, \cdot)\)	n/a	192	2
2520.2.cl	\(\chi_{2520}(2221, \cdot)\)	n/a	768	2
2520.2.cm	\(\chi_{2520}(31, \cdot)\)	None	0	2
2520.2.cn	\(\chi_{2520}(851, \cdot)\)	n/a	768	2
2520.2.cs	\(\chi_{2520}(19, \cdot)\)	n/a	472	2
2520.2.ct	\(\chi_{2520}(359, \cdot)\)	None	0	2
2520.2.cu	\(\chi_{2520}(269, \cdot)\)	n/a	384	2
2520.2.cv	\(\chi_{2520}(289, \cdot)\)	n/a	120	2
2520.2.cy	\(\chi_{2520}(911, \cdot)\)	None	0	2
2520.2.cz	\(\chi_{2520}(1651, \cdot)\)	n/a	768	2
2520.2.dc	\(\chi_{2520}(101, \cdot)\)	n/a	768	2
2520.2.dh	\(\chi_{2520}(1031, \cdot)\)	None	0	2
2520.2.di	\(\chi_{2520}(2131, \cdot)\)	n/a	768	2
2520.2.dl	\(\chi_{2520}(461, \cdot)\)	n/a	768	2
2520.2.do	\(\chi_{2520}(1469, \cdot)\)	n/a	1136	2
2520.2.dp	\(\chi_{2520}(169, \cdot)\)	n/a	216	2
2520.2.ds	\(\chi_{2520}(619, \cdot)\)	n/a	1136	2
2520.2.dt	\(\chi_{2520}(2039, \cdot)\)	None	0	2
2520.2.du	\(\chi_{2520}(509, \cdot)\)	n/a	1136	2
2520.2.dv	\(\chi_{2520}(529, \cdot)\)	n/a	288	2
2520.2.dy	\(\chi_{2520}(139, \cdot)\)	n/a	1136	2
2520.2.dz	\(\chi_{2520}(239, \cdot)\)	None	0	2
2520.2.ec	\(\chi_{2520}(341, \cdot)\)	n/a	256	2
2520.2.eh	\(\chi_{2520}(431, \cdot)\)	None	0	2
2520.2.ei	\(\chi_{2520}(451, \cdot)\)	n/a	320	2
2520.2.el	\(\chi_{2520}(541, \cdot)\)	n/a	320	2
2520.2.em	\(\chi_{2520}(521, \cdot)\)	2520.2.em.a	32	2
		2520.2.em.b	32
2520.2.en	\(\chi_{2520}(611, \cdot)\)	n/a	256	2
2520.2.eo	\(\chi_{2520}(271, \cdot)\)	None	0	2
2520.2.er	\(\chi_{2520}(209, \cdot)\)	n/a	288	2
2520.2.es	\(\chi_{2520}(589, \cdot)\)	n/a	864	2
2520.2.ev	\(\chi_{2520}(1879, \cdot)\)	None	0	2
2520.2.ew	\(\chi_{2520}(779, \cdot)\)	n/a	1136	2
2520.2.fb	\(\chi_{2520}(1769, \cdot)\)	n/a	288	2
2520.2.fc	\(\chi_{2520}(1789, \cdot)\)	n/a	1136	2
2520.2.ff	\(\chi_{2520}(1399, \cdot)\)	None	0	2
2520.2.fg	\(\chi_{2520}(659, \cdot)\)	n/a	864	2
2520.2.fj	\(\chi_{2520}(491, \cdot)\)	n/a	576	2
2520.2.fk	\(\chi_{2520}(391, \cdot)\)	None	0	2
2520.2.fn	\(\chi_{2520}(781, \cdot)\)	n/a	768	2
2520.2.fo	\(\chi_{2520}(761, \cdot)\)	n/a	192	2
2520.2.fp	\(\chi_{2520}(11, \cdot)\)	n/a	768	2
2520.2.fq	\(\chi_{2520}(871, \cdot)\)	None	0	2
2520.2.ft	\(\chi_{2520}(421, \cdot)\)	n/a	576	2
2520.2.fu	\(\chi_{2520}(41, \cdot)\)	n/a	192	2
2520.2.fx	\(\chi_{2520}(199, \cdot)\)	None	0	2
2520.2.fy	\(\chi_{2520}(179, \cdot)\)	n/a	384	2
2520.2.gd	\(\chi_{2520}(89, \cdot)\)	2520.2.gd.a	48	2
		2520.2.gd.b	48
2520.2.ge	\(\chi_{2520}(109, \cdot)\)	n/a	472	2
2520.2.gf	\(\chi_{2520}(941, \cdot)\)	n/a	768	2
2520.2.gk	\(\chi_{2520}(691, \cdot)\)	n/a	768	2
2520.2.gl	\(\chi_{2520}(191, \cdot)\)	None	0	2
2520.2.go	\(\chi_{2520}(599, \cdot)\)	None	0	2
2520.2.gp	\(\chi_{2520}(1699, \cdot)\)	n/a	1136	2
2520.2.gq	\(\chi_{2520}(1969, \cdot)\)	n/a	288	2
2520.2.gr	\(\chi_{2520}(1949, \cdot)\)	n/a	1136	2
2520.2.gw	\(\chi_{2520}(563, \cdot)\)	n/a	2272	4
2520.2.gx	\(\chi_{2520}(583, \cdot)\)	None	0	4
2520.2.gy	\(\chi_{2520}(473, \cdot)\)	n/a	576	4
2520.2.gz	\(\chi_{2520}(157, \cdot)\)	n/a	2272	4
2520.2.hc	\(\chi_{2520}(167, \cdot)\)	None	0	4
2520.2.hd	\(\chi_{2520}(43, \cdot)\)	n/a	1728	4
2520.2.hg	\(\chi_{2520}(53, \cdot)\)	n/a	768	4
2520.2.hh	\(\chi_{2520}(73, \cdot)\)	n/a	240	4
2520.2.hk	\(\chi_{2520}(1753, \cdot)\)	n/a	576	4
2520.2.hl	\(\chi_{2520}(653, \cdot)\)	n/a	2272	4
2520.2.hq	\(\chi_{2520}(403, \cdot)\)	n/a	2272	4
2520.2.hr	\(\chi_{2520}(383, \cdot)\)	None	0	4
2520.2.hu	\(\chi_{2520}(143, \cdot)\)	None	0	4
2520.2.hv	\(\chi_{2520}(163, \cdot)\)	n/a	944	4
2520.2.hy	\(\chi_{2520}(533, \cdot)\)	n/a	1728	4
2520.2.hz	\(\chi_{2520}(97, \cdot)\)	n/a	576	4
2520.2.ia	\(\chi_{2520}(113, \cdot)\)	n/a	432	4
2520.2.ib	\(\chi_{2520}(13, \cdot)\)	n/a	2272	4
2520.2.ie	\(\chi_{2520}(467, \cdot)\)	n/a	768	4
2520.2.if	\(\chi_{2520}(487, \cdot)\)	None	0	4
2520.2.ii	\(\chi_{2520}(247, \cdot)\)	None	0	4
2520.2.ij	\(\chi_{2520}(227, \cdot)\)	n/a	2272	4
2520.2.io	\(\chi_{2520}(493, \cdot)\)	n/a	2272	4
2520.2.ip	\(\chi_{2520}(137, \cdot)\)	n/a	576	4
2520.2.is	\(\chi_{2520}(233, \cdot)\)	n/a	192	4
2520.2.it	\(\chi_{2520}(397, \cdot)\)	n/a	944	4
2520.2.iw	\(\chi_{2520}(83, \cdot)\)	n/a	2272	4
2520.2.ix	\(\chi_{2520}(463, \cdot)\)	None	0	4
2520.2.ja	\(\chi_{2520}(317, \cdot)\)	n/a	2272	4
2520.2.jb	\(\chi_{2520}(313, \cdot)\)	n/a	576	4
2520.2.jc	\(\chi_{2520}(47, \cdot)\)	None	0	4
2520.2.jd	\(\chi_{2520}(67, \cdot)\)	n/a	2272	4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2520))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2520)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(56))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(168))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(280))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(315))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(420))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(504))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(630))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(840))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1260))\)\(^{\oplus 2}\)