Space of modular forms of level 2340 and weight 2

• Label: 2340.2
• Level: 2340
• Weight: 2
• Dimension: 60124
• Nonzero newspaces: 100
• Sturm bound: 580608
• Trace bound: 37

Defining parameters

Level:	\( N \)	=	\( 2340 = 2^{2} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 100 \)
Sturm bound:			\(580608\)
Trace bound:			\(37\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2340))\).

	Total	New	Old
Modular forms	148992	61308	87684
Cusp forms	141313	60124	81189
Eisenstein series	7679	1184	6495

Trace form

60124 * q - 36 * q^2 - 48 * q^4 - 100 * q^5 - 124 * q^6 - 12 * q^7 - 36 * q^8 - 120 * q^9 - 150 * q^10 - 32 * q^11 - 8 * q^12 - 70 * q^13 - 6 * q^15 - 48 * q^16 - 50 * q^17 + 56 * q^18 - 32 * q^19 + 38 * q^20 - 236 * q^21 - 12 * q^22 + 24 * q^23 + 36 * q^24 - 92 * q^25 - 100 * q^26 + 48 * q^27 - 56 * q^28 - 30 * q^29 - 12 * q^30 - 72 * q^31 - 76 * q^32 - 12 * q^33 + 10 * q^35 - 180 * q^36 - 242 * q^37 - 20 * q^38 - 46 * q^39 - 226 * q^41 - 80 * q^42 - 92 * q^43 + 24 * q^44 + 18 * q^45 - 124 * q^46 - 12 * q^47 + 20 * q^48 - 146 * q^49 - 16 * q^50 + 48 * q^51 + 64 * q^52 - 32 * q^53 + 20 * q^54 - 26 * q^55 - 136 * q^56 + 104 * q^57 + 20 * q^58 + 16 * q^59 - 104 * q^60 - 138 * q^61 - 68 * q^62 + 92 * q^63 + 72 * q^64 - 68 * q^65 - 224 * q^66 + 48 * q^67 + 164 * q^68 - 20 * q^69 + 108 * q^70 + 96 * q^71 - 12 * q^72 - 40 * q^73 + 204 * q^74 - 18 * q^75 + 304 * q^76 + 228 * q^77 + 256 * q^78 + 108 * q^79 + 64 * q^80 - 288 * q^81 + 404 * q^82 + 228 * q^83 + 88 * q^84 + 183 * q^85 + 364 * q^86 - 68 * q^87 + 540 * q^88 + 20 * q^89 - 192 * q^90 + 148 * q^91 + 248 * q^92 + 52 * q^93 + 372 * q^94 - 96 * q^95 - 280 * q^96 + 68 * q^97 + 72 * q^98 - 44 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2340))\)

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
2340.2.a	\(\chi_{2340}(1, \cdot)\)	2340.2.a.a	1	1
		2340.2.a.b	1
		2340.2.a.c	1
		2340.2.a.d	1
		2340.2.a.e	1
		2340.2.a.f	1
		2340.2.a.g	1
		2340.2.a.h	1
		2340.2.a.i	1
		2340.2.a.j	2
		2340.2.a.k	2
		2340.2.a.l	2
		2340.2.a.m	2
		2340.2.a.n	3
2340.2.c	\(\chi_{2340}(181, \cdot)\)	2340.2.c.a	2	1
		2340.2.c.b	2
		2340.2.c.c	4
		2340.2.c.d	6
		2340.2.c.e	8
2340.2.d	\(\chi_{2340}(2339, \cdot)\)	n/a	168	1
2340.2.g	\(\chi_{2340}(1691, \cdot)\)	2340.2.g.a	48	1
		2340.2.g.b	48
2340.2.h	\(\chi_{2340}(469, \cdot)\)	2340.2.h.a	2	1
		2340.2.h.b	2
		2340.2.h.c	4
		2340.2.h.d	4
		2340.2.h.e	6
		2340.2.h.f	12
2340.2.j	\(\chi_{2340}(649, \cdot)\)	2340.2.j.a	4	1
		2340.2.j.b	4
		2340.2.j.c	8
		2340.2.j.d	8
		2340.2.j.e	12
2340.2.m	\(\chi_{2340}(1871, \cdot)\)	n/a	112	1
2340.2.n	\(\chi_{2340}(2159, \cdot)\)	n/a	144	1
2340.2.q	\(\chi_{2340}(1621, \cdot)\)	2340.2.q.a	2	2
		2340.2.q.b	2
		2340.2.q.c	2
		2340.2.q.d	2
		2340.2.q.e	2
		2340.2.q.f	2
		2340.2.q.g	4
		2340.2.q.h	6
		2340.2.q.i	6
		2340.2.q.j	10
		2340.2.q.k	10
2340.2.r	\(\chi_{2340}(781, \cdot)\)	2340.2.r.a	2	2
		2340.2.r.b	2
		2340.2.r.c	2
		2340.2.r.d	14
		2340.2.r.e	20
		2340.2.r.f	26
		2340.2.r.g	30
2340.2.s	\(\chi_{2340}(601, \cdot)\)	n/a	112	2
2340.2.t	\(\chi_{2340}(61, \cdot)\)	n/a	112	2
2340.2.u	\(\chi_{2340}(73, \cdot)\)	2340.2.u.a	2	2
		2340.2.u.b	2
		2340.2.u.c	2
		2340.2.u.d	4
		2340.2.u.e	4
		2340.2.u.f	4
		2340.2.u.g	8
		2340.2.u.h	16
		2340.2.u.i	28
2340.2.x	\(\chi_{2340}(827, \cdot)\)	n/a	336	2
2340.2.y	\(\chi_{2340}(53, \cdot)\)	2340.2.y.a	24	2
		2340.2.y.b	24
2340.2.bb	\(\chi_{2340}(703, \cdot)\)	n/a	360	2
2340.2.bc	\(\chi_{2340}(629, \cdot)\)	2340.2.bc.a	56	2
2340.2.bf	\(\chi_{2340}(811, \cdot)\)	n/a	280	2
2340.2.bh	\(\chi_{2340}(1279, \cdot)\)	n/a	412	2
2340.2.bi	\(\chi_{2340}(161, \cdot)\)	2340.2.bi.a	4	2
		2340.2.bi.b	4
		2340.2.bi.c	12
		2340.2.bi.d	12
2340.2.bk	\(\chi_{2340}(883, \cdot)\)	n/a	412	2
2340.2.bn	\(\chi_{2340}(233, \cdot)\)	2340.2.bn.a	56	2
2340.2.bp	\(\chi_{2340}(1477, \cdot)\)	2340.2.bp.a	2	2
		2340.2.bp.b	2
		2340.2.bp.c	2
		2340.2.bp.d	4
		2340.2.bp.e	4
		2340.2.bp.f	4
		2340.2.bp.g	8
		2340.2.bp.h	16
		2340.2.bp.i	28
2340.2.bq	\(\chi_{2340}(1763, \cdot)\)	n/a	336	2
2340.2.bs	\(\chi_{2340}(529, \cdot)\)	n/a	168	2
2340.2.bv	\(\chi_{2340}(191, \cdot)\)	n/a	672	2
2340.2.bw	\(\chi_{2340}(959, \cdot)\)	n/a	992	2
2340.2.bz	\(\chi_{2340}(1681, \cdot)\)	n/a	112	2
2340.2.ca	\(\chi_{2340}(1031, \cdot)\)	n/a	672	2
2340.2.cd	\(\chi_{2340}(589, \cdot)\)	n/a	168	2
2340.2.cg	\(\chi_{2340}(1439, \cdot)\)	n/a	336	2
2340.2.ci	\(\chi_{2340}(599, \cdot)\)	n/a	864	2
2340.2.cl	\(\chi_{2340}(1429, \cdot)\)	n/a	168	2
2340.2.cm	\(\chi_{2340}(311, \cdot)\)	n/a	672	2
2340.2.co	\(\chi_{2340}(251, \cdot)\)	n/a	224	2
2340.2.cr	\(\chi_{2340}(829, \cdot)\)	2340.2.cr.a	16	2
		2340.2.cr.b	24
		2340.2.cr.c	32
2340.2.cu	\(\chi_{2340}(1199, \cdot)\)	n/a	992	2
2340.2.cw	\(\chi_{2340}(1499, \cdot)\)	n/a	992	2
2340.2.cx	\(\chi_{2340}(121, \cdot)\)	n/a	112	2
2340.2.cz	\(\chi_{2340}(131, \cdot)\)	n/a	576	2
2340.2.dc	\(\chi_{2340}(1249, \cdot)\)	n/a	144	2
2340.2.de	\(\chi_{2340}(289, \cdot)\)	2340.2.de.a	12	2
		2340.2.de.b	24
		2340.2.de.c	32
2340.2.df	\(\chi_{2340}(971, \cdot)\)	n/a	224	2
2340.2.di	\(\chi_{2340}(179, \cdot)\)	n/a	336	2
2340.2.dj	\(\chi_{2340}(361, \cdot)\)	2340.2.dj.a	4	2
		2340.2.dj.b	8
		2340.2.dj.c	8
		2340.2.dj.d	8
		2340.2.dj.e	20
2340.2.dl	\(\chi_{2340}(961, \cdot)\)	n/a	112	2
2340.2.do	\(\chi_{2340}(779, \cdot)\)	n/a	992	2
2340.2.dq	\(\chi_{2340}(1069, \cdot)\)	n/a	168	2
2340.2.dr	\(\chi_{2340}(731, \cdot)\)	n/a	672	2
2340.2.du	\(\chi_{2340}(419, \cdot)\)	n/a	992	2
2340.2.dx	\(\chi_{2340}(491, \cdot)\)	n/a	672	2
2340.2.dy	\(\chi_{2340}(49, \cdot)\)	n/a	168	2
2340.2.ea	\(\chi_{2340}(167, \cdot)\)	n/a	1984	4
2340.2.ed	\(\chi_{2340}(97, \cdot)\)	n/a	336	4
2340.2.ee	\(\chi_{2340}(817, \cdot)\)	n/a	336	4
2340.2.eg	\(\chi_{2340}(203, \cdot)\)	n/a	1984	4
2340.2.ei	\(\chi_{2340}(323, \cdot)\)	n/a	672	4
2340.2.el	\(\chi_{2340}(37, \cdot)\)	n/a	140	4
2340.2.en	\(\chi_{2340}(697, \cdot)\)	n/a	336	4
2340.2.ep	\(\chi_{2340}(587, \cdot)\)	n/a	1984	4
2340.2.eq	\(\chi_{2340}(367, \cdot)\)	n/a	1984	4
2340.2.et	\(\chi_{2340}(113, \cdot)\)	n/a	336	4
2340.2.ev	\(\chi_{2340}(103, \cdot)\)	n/a	1984	4
2340.2.ew	\(\chi_{2340}(17, \cdot)\)	n/a	112	4
2340.2.ez	\(\chi_{2340}(173, \cdot)\)	n/a	336	4
2340.2.fa	\(\chi_{2340}(43, \cdot)\)	n/a	1984	4
2340.2.fd	\(\chi_{2340}(127, \cdot)\)	n/a	824	4
2340.2.fe	\(\chi_{2340}(77, \cdot)\)	n/a	336	4
2340.2.fg	\(\chi_{2340}(31, \cdot)\)	n/a	1344	4
2340.2.fj	\(\chi_{2340}(749, \cdot)\)	n/a	336	4
2340.2.fk	\(\chi_{2340}(799, \cdot)\)	n/a	1984	4
2340.2.fm	\(\chi_{2340}(761, \cdot)\)	n/a	224	4
2340.2.fo	\(\chi_{2340}(1241, \cdot)\)	2340.2.fo.a	40	4
		2340.2.fo.b	40
2340.2.fr	\(\chi_{2340}(19, \cdot)\)	n/a	824	4
2340.2.ft	\(\chi_{2340}(319, \cdot)\)	n/a	1984	4
2340.2.fv	\(\chi_{2340}(41, \cdot)\)	n/a	224	4
2340.2.fx	\(\chi_{2340}(509, \cdot)\)	n/a	336	4
2340.2.fz	\(\chi_{2340}(271, \cdot)\)	n/a	560	4
2340.2.gb	\(\chi_{2340}(691, \cdot)\)	n/a	1344	4
2340.2.gc	\(\chi_{2340}(149, \cdot)\)	n/a	336	4
2340.2.ge	\(\chi_{2340}(89, \cdot)\)	n/a	112	4
2340.2.gg	\(\chi_{2340}(331, \cdot)\)	n/a	1344	4
2340.2.gj	\(\chi_{2340}(281, \cdot)\)	n/a	224	4
2340.2.gk	\(\chi_{2340}(499, \cdot)\)	n/a	1984	4
2340.2.gn	\(\chi_{2340}(677, \cdot)\)	n/a	288	4
2340.2.go	\(\chi_{2340}(523, \cdot)\)	n/a	824	4
2340.2.gr	\(\chi_{2340}(763, \cdot)\)	n/a	1984	4
2340.2.gs	\(\chi_{2340}(653, \cdot)\)	n/a	336	4
2340.2.gv	\(\chi_{2340}(737, \cdot)\)	n/a	112	4
2340.2.gw	\(\chi_{2340}(547, \cdot)\)	n/a	1728	4
2340.2.gy	\(\chi_{2340}(797, \cdot)\)	n/a	336	4
2340.2.hb	\(\chi_{2340}(823, \cdot)\)	n/a	1984	4
2340.2.hd	\(\chi_{2340}(457, \cdot)\)	n/a	336	4
2340.2.hf	\(\chi_{2340}(1727, \cdot)\)	n/a	672	4
2340.2.hh	\(\chi_{2340}(47, \cdot)\)	n/a	1984	4
2340.2.hi	\(\chi_{2340}(853, \cdot)\)	n/a	336	4
2340.2.hk	\(\chi_{2340}(973, \cdot)\)	n/a	140	4
2340.2.hm	\(\chi_{2340}(383, \cdot)\)	n/a	1984	4
2340.2.hp	\(\chi_{2340}(227, \cdot)\)	n/a	1984	4
2340.2.hq	\(\chi_{2340}(1033, \cdot)\)	n/a	336	4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2340))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2340)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(780))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1170))\)\(^{\oplus 2}\)