Space of modular forms of level 2380 and weight 2

• Label: 2380.2
• Level: 2380
• Weight: 2
• Dimension: 83516
• Nonzero newspaces: 72
• Sturm bound: 663552
• Trace bound: 33

Defining parameters

Level:	\( N \)	=	\( 2380 = 2^{2} \cdot 5 \cdot 7 \cdot 17 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 72 \)
Sturm bound:			\(663552\)
Trace bound:			\(33\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2380))\).

	Total	New	Old
Modular forms	169728	85324	84404
Cusp forms	162049	83516	78533
Eisenstein series	7679	1808	5871

Trace form

83516 * q - 60 * q^2 - 12 * q^3 - 52 * q^4 - 182 * q^5 - 144 * q^6 - 12 * q^7 - 108 * q^8 - 92 * q^9 - 36 * q^10 - 20 * q^11 + 8 * q^12 - 96 * q^13 - 20 * q^14 - 28 * q^15 - 108 * q^16 - 154 * q^17 - 116 * q^18 - 44 * q^19 - 88 * q^20 - 420 * q^21 - 184 * q^22 - 20 * q^23 - 24 * q^24 - 54 * q^25 - 48 * q^26 + 144 * q^27 - 68 * q^28 - 72 * q^29 + 44 * q^30 + 188 * q^31 + 140 * q^32 + 268 * q^33 + 192 * q^34 + 130 * q^35 - 44 * q^36 + 100 * q^37 + 192 * q^38 + 160 * q^39 + 64 * q^40 - 248 * q^41 + 88 * q^42 + 8 * q^43 + 160 * q^44 - 64 * q^45 - 32 * q^46 - 124 * q^47 - 136 * q^48 - 260 * q^49 - 196 * q^50 - 110 * q^51 - 216 * q^52 - 196 * q^53 - 320 * q^54 - 116 * q^55 - 332 * q^56 - 248 * q^57 - 448 * q^58 - 148 * q^59 - 544 * q^60 - 268 * q^61 - 480 * q^62 - 180 * q^63 - 556 * q^64 - 92 * q^65 - 808 * q^66 - 92 * q^67 - 560 * q^68 - 24 * q^69 - 516 * q^70 - 16 * q^71 - 924 * q^72 + 364 * q^73 - 544 * q^74 + 90 * q^75 - 656 * q^76 - 12 * q^77 - 720 * q^78 + 84 * q^79 - 304 * q^80 + 136 * q^81 - 328 * q^82 + 216 * q^83 - 264 * q^84 - 98 * q^85 - 184 * q^86 + 384 * q^87 + 96 * q^88 + 460 * q^89 - 32 * q^90 + 296 * q^91 + 312 * q^92 + 556 * q^93 + 224 * q^94 + 566 * q^95 + 368 * q^96 + 352 * q^97 + 212 * q^98 + 816 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2380))\)

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
2380.2.a	\(\chi_{2380}(1, \cdot)\)	2380.2.a.a	1	1
		2380.2.a.b	3
		2380.2.a.c	3
		2380.2.a.d	4
		2380.2.a.e	4
		2380.2.a.f	4
		2380.2.a.g	4
		2380.2.a.h	4
		2380.2.a.i	5
2380.2.d	\(\chi_{2380}(1121, \cdot)\)	2380.2.d.a	2	1
		2380.2.d.b	2
		2380.2.d.c	2
		2380.2.d.d	12
		2380.2.d.e	18
2380.2.e	\(\chi_{2380}(1259, \cdot)\)	n/a	384	1
2380.2.h	\(\chi_{2380}(1429, \cdot)\)	2380.2.h.a	2	1
		2380.2.h.b	2
		2380.2.h.c	20
		2380.2.h.d	24
2380.2.i	\(\chi_{2380}(951, \cdot)\)	n/a	288	1
2380.2.l	\(\chi_{2380}(2211, \cdot)\)	n/a	256	1
2380.2.m	\(\chi_{2380}(169, \cdot)\)	2380.2.m.a	2	1
		2380.2.m.b	2
		2380.2.m.c	26
		2380.2.m.d	26
2380.2.p	\(\chi_{2380}(2379, \cdot)\)	n/a	424	1
2380.2.q	\(\chi_{2380}(681, \cdot)\)	2380.2.q.a	2	2
		2380.2.q.b	2
		2380.2.q.c	4
		2380.2.q.d	4
		2380.2.q.e	6
		2380.2.q.f	18
		2380.2.q.g	24
		2380.2.q.h	28
2380.2.r	\(\chi_{2380}(293, \cdot)\)	n/a	144	2
2380.2.s	\(\chi_{2380}(463, \cdot)\)	n/a	648	2
2380.2.x	\(\chi_{2380}(1667, \cdot)\)	n/a	576	2
2380.2.y	\(\chi_{2380}(237, \cdot)\)	n/a	144	2
2380.2.z	\(\chi_{2380}(1849, \cdot)\)	n/a	112	2
2380.2.ba	\(\chi_{2380}(251, \cdot)\)	n/a	576	2
2380.2.bd	\(\chi_{2380}(1679, \cdot)\)	n/a	848	2
2380.2.be	\(\chi_{2380}(421, \cdot)\)	2380.2.be.a	4	2
		2380.2.be.b	32
		2380.2.be.c	36
2380.2.bj	\(\chi_{2380}(1497, \cdot)\)	n/a	128	2
2380.2.bk	\(\chi_{2380}(407, \cdot)\)	n/a	648	2
2380.2.bl	\(\chi_{2380}(183, \cdot)\)	n/a	648	2
2380.2.bm	\(\chi_{2380}(13, \cdot)\)	n/a	144	2
2380.2.bp	\(\chi_{2380}(339, \cdot)\)	n/a	848	2
2380.2.bs	\(\chi_{2380}(849, \cdot)\)	n/a	144	2
2380.2.bt	\(\chi_{2380}(171, \cdot)\)	n/a	512	2
2380.2.bw	\(\chi_{2380}(271, \cdot)\)	n/a	576	2
2380.2.bx	\(\chi_{2380}(1089, \cdot)\)	n/a	128	2
2380.2.ca	\(\chi_{2380}(579, \cdot)\)	n/a	768	2
2380.2.cb	\(\chi_{2380}(781, \cdot)\)	2380.2.cb.a	4	2
		2380.2.cb.b	92
2380.2.cf	\(\chi_{2380}(281, \cdot)\)	n/a	144	4
2380.2.ch	\(\chi_{2380}(559, \cdot)\)	n/a	1696	4
2380.2.ci	\(\chi_{2380}(127, \cdot)\)	n/a	1296	4
2380.2.cl	\(\chi_{2380}(433, \cdot)\)	n/a	288	4
2380.2.cn	\(\chi_{2380}(1273, \cdot)\)	n/a	288	4
2380.2.co	\(\chi_{2380}(43, \cdot)\)	n/a	1296	4
2380.2.cq	\(\chi_{2380}(111, \cdot)\)	n/a	1152	4
2380.2.cs	\(\chi_{2380}(729, \cdot)\)	n/a	208	4
2380.2.cw	\(\chi_{2380}(157, \cdot)\)	n/a	288	4
2380.2.cx	\(\chi_{2380}(667, \cdot)\)	n/a	1696	4
2380.2.cy	\(\chi_{2380}(817, \cdot)\)	n/a	256	4
2380.2.cz	\(\chi_{2380}(67, \cdot)\)	n/a	1696	4
2380.2.de	\(\chi_{2380}(591, \cdot)\)	n/a	1152	4
2380.2.df	\(\chi_{2380}(149, \cdot)\)	n/a	288	4
2380.2.di	\(\chi_{2380}(81, \cdot)\)	n/a	192	4
2380.2.dj	\(\chi_{2380}(999, \cdot)\)	n/a	1696	4
2380.2.dk	\(\chi_{2380}(443, \cdot)\)	n/a	1536	4
2380.2.dl	\(\chi_{2380}(33, \cdot)\)	n/a	288	4
2380.2.dq	\(\chi_{2380}(123, \cdot)\)	n/a	1696	4
2380.2.dr	\(\chi_{2380}(633, \cdot)\)	n/a	288	4
2380.2.dt	\(\chi_{2380}(167, \cdot)\)	n/a	3392	8
2380.2.du	\(\chi_{2380}(57, \cdot)\)	n/a	432	8
2380.2.dy	\(\chi_{2380}(209, \cdot)\)	n/a	576	8
2380.2.dz	\(\chi_{2380}(71, \cdot)\)	n/a	1728	8
2380.2.ea	\(\chi_{2380}(41, \cdot)\)	n/a	384	8
2380.2.eb	\(\chi_{2380}(99, \cdot)\)	n/a	2592	8
2380.2.ee	\(\chi_{2380}(113, \cdot)\)	n/a	432	8
2380.2.eh	\(\chi_{2380}(27, \cdot)\)	n/a	3392	8
2380.2.ei	\(\chi_{2380}(19, \cdot)\)	n/a	3392	8
2380.2.ek	\(\chi_{2380}(121, \cdot)\)	n/a	384	8
2380.2.en	\(\chi_{2380}(117, \cdot)\)	n/a	576	8
2380.2.eo	\(\chi_{2380}(247, \cdot)\)	n/a	3392	8
2380.2.eq	\(\chi_{2380}(263, \cdot)\)	n/a	3392	8
2380.2.et	\(\chi_{2380}(297, \cdot)\)	n/a	576	8
2380.2.ev	\(\chi_{2380}(9, \cdot)\)	n/a	576	8
2380.2.ex	\(\chi_{2380}(451, \cdot)\)	n/a	2304	8
2380.2.ey	\(\chi_{2380}(177, \cdot)\)	n/a	1152	16
2380.2.fb	\(\chi_{2380}(143, \cdot)\)	n/a	6784	16
2380.2.fe	\(\chi_{2380}(61, \cdot)\)	n/a	768	16
2380.2.ff	\(\chi_{2380}(39, \cdot)\)	n/a	6784	16
2380.2.fg	\(\chi_{2380}(129, \cdot)\)	n/a	1152	16
2380.2.fh	\(\chi_{2380}(11, \cdot)\)	n/a	4608	16
2380.2.fl	\(\chi_{2380}(3, \cdot)\)	n/a	6784	16
2380.2.fm	\(\chi_{2380}(37, \cdot)\)	n/a	1152	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2380))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2380)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(85))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(140))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(170))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(340))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(595))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1190))\)\(^{\oplus 2}\)