Space of modular forms of level 2320 and weight 2

• Label: 2320.2
• Level: 2320
• Weight: 2
• Dimension: 82232
• Nonzero newspaces: 52
• Sturm bound: 645120
• Trace bound: 13

Defining parameters

Level:	\( N \)	=	\( 2320 = 2^{4} \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 52 \)
Sturm bound:			\(645120\)
Trace bound:			\(13\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2320))\).

	Total	New	Old
Modular forms	164416	83692	80724
Cusp forms	158145	82232	75913
Eisenstein series	6271	1460	4811

Trace form

82232 * q - 104 * q^2 - 80 * q^3 - 96 * q^4 - 194 * q^5 - 288 * q^6 - 72 * q^7 - 80 * q^8 - 20 * q^9 - 152 * q^10 - 220 * q^11 - 112 * q^12 - 120 * q^13 - 112 * q^14 - 82 * q^15 - 336 * q^16 - 216 * q^17 - 88 * q^18 - 28 * q^19 - 144 * q^20 - 332 * q^21 - 96 * q^22 - 48 * q^23 - 96 * q^24 - 22 * q^25 - 288 * q^26 - 92 * q^27 - 128 * q^28 - 120 * q^29 - 392 * q^30 - 308 * q^31 - 144 * q^32 - 284 * q^33 - 208 * q^34 - 146 * q^35 - 448 * q^36 - 176 * q^37 - 256 * q^38 - 124 * q^39 - 328 * q^40 - 140 * q^41 - 256 * q^42 - 64 * q^43 - 224 * q^44 - 246 * q^45 - 384 * q^46 - 8 * q^47 - 192 * q^48 - 220 * q^49 - 264 * q^50 - 180 * q^51 - 176 * q^52 - 128 * q^53 - 192 * q^54 - 86 * q^55 - 336 * q^56 + 80 * q^57 - 128 * q^58 - 112 * q^59 - 88 * q^60 - 420 * q^61 - 32 * q^62 - 136 * q^63 - 48 * q^64 - 278 * q^65 - 160 * q^66 - 184 * q^67 + 16 * q^68 - 164 * q^69 + 8 * q^70 - 340 * q^71 + 160 * q^72 + 16 * q^73 + 80 * q^74 - 338 * q^75 - 128 * q^76 - 124 * q^77 + 160 * q^78 - 260 * q^79 + 24 * q^80 - 640 * q^81 + 32 * q^82 - 256 * q^83 + 176 * q^84 - 190 * q^85 - 176 * q^86 - 200 * q^87 + 20 * q^89 + 80 * q^90 - 276 * q^91 - 112 * q^92 - 28 * q^93 - 48 * q^94 - 230 * q^95 - 240 * q^96 - 64 * q^97 - 184 * q^98 + 108 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2320))\)

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
2320.2.a	\(\chi_{2320}(1, \cdot)\)	2320.2.a.a	1	1
		2320.2.a.b	1
		2320.2.a.c	1
		2320.2.a.d	1
		2320.2.a.e	1
		2320.2.a.f	1
		2320.2.a.g	1
		2320.2.a.h	1
		2320.2.a.i	2
		2320.2.a.j	2
		2320.2.a.k	2
		2320.2.a.l	3
		2320.2.a.m	3
		2320.2.a.n	3
		2320.2.a.o	3
		2320.2.a.p	3
		2320.2.a.q	3
		2320.2.a.r	3
		2320.2.a.s	3
		2320.2.a.t	3
		2320.2.a.u	5
		2320.2.a.v	5
		2320.2.a.w	5
2320.2.d	\(\chi_{2320}(929, \cdot)\)	2320.2.d.a	2	1
		2320.2.d.b	2
		2320.2.d.c	4
		2320.2.d.d	4
		2320.2.d.e	4
		2320.2.d.f	4
		2320.2.d.g	6
		2320.2.d.h	10
		2320.2.d.i	10
		2320.2.d.j	16
		2320.2.d.k	22
2320.2.e	\(\chi_{2320}(1449, \cdot)\)	None	0	1
2320.2.f	\(\chi_{2320}(1161, \cdot)\)	None	0	1
2320.2.g	\(\chi_{2320}(1681, \cdot)\)	2320.2.g.a	2	1
		2320.2.g.b	2
		2320.2.g.c	2
		2320.2.g.d	4
		2320.2.g.e	4
		2320.2.g.f	4
		2320.2.g.g	4
		2320.2.g.h	4
		2320.2.g.i	6
		2320.2.g.j	14
		2320.2.g.k	14
2320.2.j	\(\chi_{2320}(289, \cdot)\)	2320.2.j.a	4	1
		2320.2.j.b	4
		2320.2.j.c	4
		2320.2.j.d	8
		2320.2.j.e	8
		2320.2.j.f	16
		2320.2.j.g	22
		2320.2.j.h	22
2320.2.k	\(\chi_{2320}(2089, \cdot)\)	None	0	1
2320.2.p	\(\chi_{2320}(521, \cdot)\)	None	0	1
2320.2.q	\(\chi_{2320}(99, \cdot)\)	n/a	712	2
2320.2.t	\(\chi_{2320}(347, \cdot)\)	n/a	712	2
2320.2.u	\(\chi_{2320}(713, \cdot)\)	None	0	2
2320.2.w	\(\chi_{2320}(17, \cdot)\)	n/a	176	2
2320.2.z	\(\chi_{2320}(523, \cdot)\)	n/a	672	2
2320.2.bb	\(\chi_{2320}(331, \cdot)\)	n/a	480	2
2320.2.bc	\(\chi_{2320}(191, \cdot)\)	n/a	120	2
2320.2.bf	\(\chi_{2320}(1101, \cdot)\)	n/a	480	2
2320.2.bh	\(\chi_{2320}(581, \cdot)\)	n/a	448	2
2320.2.bi	\(\chi_{2320}(1351, \cdot)\)	None	0	2
2320.2.bl	\(\chi_{2320}(853, \cdot)\)	n/a	712	2
2320.2.bo	\(\chi_{2320}(1103, \cdot)\)	n/a	168	2
2320.2.bp	\(\chi_{2320}(1623, \cdot)\)	None	0	2
2320.2.bq	\(\chi_{2320}(1293, \cdot)\)	n/a	712	2
2320.2.bs	\(\chi_{2320}(133, \cdot)\)	n/a	712	2
2320.2.bu	\(\chi_{2320}(407, \cdot)\)	None	0	2
2320.2.bv	\(\chi_{2320}(463, \cdot)\)	n/a	180	2
2320.2.bz	\(\chi_{2320}(597, \cdot)\)	n/a	712	2
2320.2.cb	\(\chi_{2320}(679, \cdot)\)	None	0	2
2320.2.cc	\(\chi_{2320}(349, \cdot)\)	n/a	672	2
2320.2.ce	\(\chi_{2320}(869, \cdot)\)	n/a	712	2
2320.2.ch	\(\chi_{2320}(1119, \cdot)\)	n/a	180	2
2320.2.cj	\(\chi_{2320}(1259, \cdot)\)	n/a	712	2
2320.2.ck	\(\chi_{2320}(987, \cdot)\)	n/a	672	2
2320.2.cn	\(\chi_{2320}(737, \cdot)\)	n/a	176	2
2320.2.cp	\(\chi_{2320}(1177, \cdot)\)	None	0	2
2320.2.cq	\(\chi_{2320}(1507, \cdot)\)	n/a	712	2
2320.2.cs	\(\chi_{2320}(1491, \cdot)\)	n/a	480	2
2320.2.cu	\(\chi_{2320}(81, \cdot)\)	n/a	360	6
2320.2.cv	\(\chi_{2320}(121, \cdot)\)	None	0	6
2320.2.da	\(\chi_{2320}(169, \cdot)\)	None	0	6
2320.2.db	\(\chi_{2320}(129, \cdot)\)	n/a	528	6
2320.2.de	\(\chi_{2320}(241, \cdot)\)	n/a	360	6
2320.2.df	\(\chi_{2320}(281, \cdot)\)	None	0	6
2320.2.dg	\(\chi_{2320}(9, \cdot)\)	None	0	6
2320.2.dh	\(\chi_{2320}(49, \cdot)\)	n/a	528	6
2320.2.dl	\(\chi_{2320}(11, \cdot)\)	n/a	2880	12
2320.2.dn	\(\chi_{2320}(67, \cdot)\)	n/a	4272	12
2320.2.do	\(\chi_{2320}(97, \cdot)\)	n/a	1056	12
2320.2.dq	\(\chi_{2320}(73, \cdot)\)	None	0	12
2320.2.dt	\(\chi_{2320}(83, \cdot)\)	n/a	4272	12
2320.2.du	\(\chi_{2320}(19, \cdot)\)	n/a	4272	12
2320.2.dw	\(\chi_{2320}(79, \cdot)\)	n/a	1080	12
2320.2.dz	\(\chi_{2320}(429, \cdot)\)	n/a	4272	12
2320.2.eb	\(\chi_{2320}(109, \cdot)\)	n/a	4272	12
2320.2.ec	\(\chi_{2320}(39, \cdot)\)	None	0	12
2320.2.ef	\(\chi_{2320}(437, \cdot)\)	n/a	4272	12
2320.2.ei	\(\chi_{2320}(63, \cdot)\)	n/a	1080	12
2320.2.ej	\(\chi_{2320}(7, \cdot)\)	None	0	12
2320.2.ek	\(\chi_{2320}(293, \cdot)\)	n/a	4272	12
2320.2.em	\(\chi_{2320}(37, \cdot)\)	n/a	4272	12
2320.2.eo	\(\chi_{2320}(167, \cdot)\)	None	0	12
2320.2.ep	\(\chi_{2320}(223, \cdot)\)	n/a	1080	12
2320.2.et	\(\chi_{2320}(77, \cdot)\)	n/a	4272	12
2320.2.ev	\(\chi_{2320}(311, \cdot)\)	None	0	12
2320.2.ew	\(\chi_{2320}(341, \cdot)\)	n/a	2880	12
2320.2.ey	\(\chi_{2320}(141, \cdot)\)	n/a	2880	12
2320.2.fb	\(\chi_{2320}(31, \cdot)\)	n/a	720	12
2320.2.fc	\(\chi_{2320}(171, \cdot)\)	n/a	2880	12
2320.2.fe	\(\chi_{2320}(123, \cdot)\)	n/a	4272	12
2320.2.fh	\(\chi_{2320}(537, \cdot)\)	None	0	12
2320.2.fj	\(\chi_{2320}(113, \cdot)\)	n/a	1056	12
2320.2.fk	\(\chi_{2320}(187, \cdot)\)	n/a	4272	12
2320.2.fn	\(\chi_{2320}(259, \cdot)\)	n/a	4272	12

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2320))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2320)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(116))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(232))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(464))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(580))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1160))\)\(^{\oplus 2}\)