Space of modular forms of level 2790 and weight 2

• Label: 2790.2
• Level: 2790
• Weight: 2
• Dimension: 50054
• Nonzero newspaces: 60
• Sturm bound: 829440
• Trace bound: 18

Defining parameters

Level:	\( N \)	=	\( 2790 = 2 \cdot 3^{2} \cdot 5 \cdot 31 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 60 \)
Sturm bound:			\(829440\)
Trace bound:			\(18\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2790))\).

	Total	New	Old
Modular forms	211200	50054	161146
Cusp forms	203521	50054	153467
Eisenstein series	7679	0	7679

Trace form

50054 * q - 6 * q^2 - 12 * q^3 - 6 * q^4 - 10 * q^5 + 12 * q^6 - 24 * q^7 + 6 * q^8 + 28 * q^9 + 22 * q^10 + 52 * q^11 + 16 * q^12 + 28 * q^13 + 40 * q^14 + 48 * q^15 - 6 * q^16 + 36 * q^17 + 8 * q^18 + 16 * q^19 + 22 * q^20 + 72 * q^21 - 40 * q^22 + 12 * q^23 - 12 * q^24 + 14 * q^25 - 72 * q^26 + 48 * q^27 - 80 * q^28 - 108 * q^29 - 112 * q^31 - 6 * q^32 - 20 * q^33 - 128 * q^34 - 92 * q^35 - 20 * q^36 - 128 * q^37 - 144 * q^38 - 128 * q^39 + 6 * q^40 - 212 * q^41 - 128 * q^42 - 40 * q^43 - 64 * q^44 - 160 * q^45 - 120 * q^47 - 20 * q^48 - 66 * q^49 - 94 * q^50 - 60 * q^51 - 20 * q^52 - 120 * q^53 - 60 * q^54 - 20 * q^55 - 40 * q^56 - 52 * q^57 - 68 * q^58 - 80 * q^59 + 16 * q^60 - 208 * q^61 + 80 * q^63 + 6 * q^64 - 6 * q^65 + 96 * q^66 - 24 * q^67 + 72 * q^68 + 128 * q^69 + 48 * q^70 + 24 * q^71 + 12 * q^72 + 56 * q^73 + 100 * q^74 + 48 * q^75 + 152 * q^76 + 504 * q^77 + 416 * q^78 + 484 * q^79 + 80 * q^80 + 476 * q^81 + 476 * q^82 + 1188 * q^83 + 264 * q^84 + 420 * q^85 + 860 * q^86 + 520 * q^87 + 380 * q^88 + 992 * q^89 + 472 * q^90 + 908 * q^91 + 72 * q^92 + 928 * q^93 + 416 * q^94 + 696 * q^95 + 16 * q^96 + 868 * q^97 + 1134 * q^98 + 640 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2790))\)

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
2790.2.a	\(\chi_{2790}(1, \cdot)\)	2790.2.a.a	1	1
		2790.2.a.b	1
		2790.2.a.c	1
		2790.2.a.d	1
		2790.2.a.e	1
		2790.2.a.f	1
		2790.2.a.g	1
		2790.2.a.h	1
		2790.2.a.i	1
		2790.2.a.j	1
		2790.2.a.k	1
		2790.2.a.l	1
		2790.2.a.m	1
		2790.2.a.n	1
		2790.2.a.o	1
		2790.2.a.p	1
		2790.2.a.q	1
		2790.2.a.r	1
		2790.2.a.s	1
		2790.2.a.t	1
		2790.2.a.u	1
		2790.2.a.v	1
		2790.2.a.w	1
		2790.2.a.x	1
		2790.2.a.y	1
		2790.2.a.z	1
		2790.2.a.ba	1
		2790.2.a.bb	1
		2790.2.a.bc	1
		2790.2.a.bd	2
		2790.2.a.be	2
		2790.2.a.bf	2
		2790.2.a.bg	2
		2790.2.a.bh	2
		2790.2.a.bi	3
		2790.2.a.bj	4
		2790.2.a.bk	4
2790.2.d	\(\chi_{2790}(559, \cdot)\)	2790.2.d.a	2	1
		2790.2.d.b	2
		2790.2.d.c	2
		2790.2.d.d	2
		2790.2.d.e	2
		2790.2.d.f	2
		2790.2.d.g	2
		2790.2.d.h	2
		2790.2.d.i	4
		2790.2.d.j	6
		2790.2.d.k	6
		2790.2.d.l	8
		2790.2.d.m	8
		2790.2.d.n	12
		2790.2.d.o	16
2790.2.e	\(\chi_{2790}(2789, \cdot)\)	2790.2.e.a	32	1
		2790.2.e.b	32
2790.2.h	\(\chi_{2790}(2231, \cdot)\)	2790.2.h.a	24	1
		2790.2.h.b	24
2790.2.i	\(\chi_{2790}(811, \cdot)\)	n/a	104	2
2790.2.j	\(\chi_{2790}(931, \cdot)\)	n/a	240	2
2790.2.k	\(\chi_{2790}(211, \cdot)\)	n/a	256	2
2790.2.l	\(\chi_{2790}(1141, \cdot)\)	n/a	256	2
2790.2.m	\(\chi_{2790}(683, \cdot)\)	n/a	120	2
2790.2.n	\(\chi_{2790}(433, \cdot)\)	n/a	160	2
2790.2.q	\(\chi_{2790}(721, \cdot)\)	n/a	224	4
2790.2.r	\(\chi_{2790}(1699, \cdot)\)	n/a	384	2
2790.2.s	\(\chi_{2790}(1049, \cdot)\)	n/a	384	2
2790.2.x	\(\chi_{2790}(161, \cdot)\)	2790.2.x.a	40	2
		2790.2.x.b	40
2790.2.y	\(\chi_{2790}(371, \cdot)\)	n/a	256	2
2790.2.bd	\(\chi_{2790}(2021, \cdot)\)	n/a	256	2
2790.2.bg	\(\chi_{2790}(929, \cdot)\)	n/a	384	2
2790.2.bh	\(\chi_{2790}(719, \cdot)\)	n/a	128	2
2790.2.bi	\(\chi_{2790}(1489, \cdot)\)	n/a	360	2
2790.2.bj	\(\chi_{2790}(1369, \cdot)\)	n/a	160	2
2790.2.bo	\(\chi_{2790}(119, \cdot)\)	n/a	384	2
2790.2.bp	\(\chi_{2790}(439, \cdot)\)	n/a	384	2
2790.2.bq	\(\chi_{2790}(491, \cdot)\)	n/a	256	2
2790.2.bt	\(\chi_{2790}(1331, \cdot)\)	n/a	192	4
2790.2.bw	\(\chi_{2790}(89, \cdot)\)	n/a	256	4
2790.2.bx	\(\chi_{2790}(109, \cdot)\)	n/a	320	4
2790.2.ca	\(\chi_{2790}(367, \cdot)\)	n/a	768	4
2790.2.cb	\(\chi_{2790}(707, \cdot)\)	n/a	768	4
2790.2.ci	\(\chi_{2790}(247, \cdot)\)	n/a	768	4
2790.2.cj	\(\chi_{2790}(497, \cdot)\)	n/a	720	4
2790.2.ck	\(\chi_{2790}(563, \cdot)\)	n/a	768	4
2790.2.cl	\(\chi_{2790}(223, \cdot)\)	n/a	768	4
2790.2.cm	\(\chi_{2790}(37, \cdot)\)	n/a	320	4
2790.2.cn	\(\chi_{2790}(377, \cdot)\)	n/a	256	4
2790.2.cq	\(\chi_{2790}(661, \cdot)\)	n/a	1024	8
2790.2.cr	\(\chi_{2790}(121, \cdot)\)	n/a	1024	8
2790.2.cs	\(\chi_{2790}(481, \cdot)\)	n/a	1024	8
2790.2.ct	\(\chi_{2790}(361, \cdot)\)	n/a	416	8
2790.2.cw	\(\chi_{2790}(523, \cdot)\)	n/a	640	8
2790.2.cx	\(\chi_{2790}(233, \cdot)\)	n/a	512	8
2790.2.da	\(\chi_{2790}(551, \cdot)\)	n/a	1024	8
2790.2.db	\(\chi_{2790}(679, \cdot)\)	n/a	1536	8
2790.2.dc	\(\chi_{2790}(569, \cdot)\)	n/a	1536	8
2790.2.dh	\(\chi_{2790}(19, \cdot)\)	n/a	640	8
2790.2.di	\(\chi_{2790}(349, \cdot)\)	n/a	1536	8
2790.2.dj	\(\chi_{2790}(179, \cdot)\)	n/a	512	8
2790.2.dk	\(\chi_{2790}(29, \cdot)\)	n/a	1536	8
2790.2.dn	\(\chi_{2790}(11, \cdot)\)	n/a	1024	8
2790.2.ds	\(\chi_{2790}(401, \cdot)\)	n/a	1024	8
2790.2.dt	\(\chi_{2790}(251, \cdot)\)	n/a	320	8
2790.2.dy	\(\chi_{2790}(239, \cdot)\)	n/a	1536	8
2790.2.dz	\(\chi_{2790}(49, \cdot)\)	n/a	1536	8
2790.2.ec	\(\chi_{2790}(107, \cdot)\)	n/a	1024	16
2790.2.ed	\(\chi_{2790}(73, \cdot)\)	n/a	1280	16
2790.2.ee	\(\chi_{2790}(13, \cdot)\)	n/a	3072	16
2790.2.ef	\(\chi_{2790}(113, \cdot)\)	n/a	3072	16
2790.2.eg	\(\chi_{2790}(47, \cdot)\)	n/a	3072	16
2790.2.eh	\(\chi_{2790}(277, \cdot)\)	n/a	3072	16
2790.2.eo	\(\chi_{2790}(173, \cdot)\)	n/a	3072	16
2790.2.ep	\(\chi_{2790}(427, \cdot)\)	n/a	3072	16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2790))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2790)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(31))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(62))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(93))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(155))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(186))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(279))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(310))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(465))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(558))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(930))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1395))\)\(^{\oplus 2}\)