Space of modular forms of level 2610 and weight 2

• Label: 2610.2
• Level: 2610
• Weight: 2
• Dimension: 43784
• Nonzero newspaces: 40
• Sturm bound: 725760
• Trace bound: 11

Defining parameters

Level:	\( N \)	=	\( 2610 = 2 \cdot 3^{2} \cdot 5 \cdot 29 \)
Weight:	\( k \)	=	\( 2 \)
Nonzero newspaces:			\( 40 \)
Sturm bound:			\(725760\)
Trace bound:			\(11\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(2610))\).

	Total	New	Old
Modular forms	185024	43784	141240
Cusp forms	177857	43784	134073
Eisenstein series	7167	0	7167

Trace form

43784 * 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 + 15 * q^20 + 72 * q^21 - 36 * q^22 + 16 * q^23 - 12 * q^24 - 22 * q^25 - 82 * q^26 + 48 * q^27 - 106 * q^29 - 96 * q^31 - 6 * q^32 - 20 * q^33 - 78 * q^34 - 88 * q^35 - 20 * q^36 - 4 * q^37 - 140 * q^38 - 128 * q^39 - q^40 - 152 * q^41 - 128 * q^42 - 20 * q^43 - 64 * q^44 - 160 * q^45 - 176 * q^47 - 20 * q^48 - 118 * q^49 - 94 * q^50 - 60 * q^51 - 20 * q^52 - 186 * q^53 - 60 * q^54 - 72 * q^55 - 40 * q^56 - 52 * q^57 - 34 * q^58 - 76 * q^59 + 16 * q^60 - 140 * q^61 + 80 * q^63 + 6 * q^64 + 21 * q^65 + 96 * q^66 - 76 * q^67 + 72 * q^68 + 128 * q^69 + 132 * q^70 + 592 * q^71 + 12 * q^72 + 382 * q^73 + 604 * q^74 + 268 * q^75 + 428 * q^76 + 864 * q^77 + 504 * q^78 + 400 * q^79 - 10 * q^80 + 892 * q^81 + 452 * q^82 + 600 * q^83 + 360 * q^84 + 564 * q^85 + 980 * q^86 + 580 * q^87 + 20 * q^88 + 932 * q^89 + 392 * q^90 + 1136 * q^91 + 576 * q^92 + 384 * q^93 + 392 * q^94 + 648 * q^95 + 16 * q^96 + 410 * q^97 + 726 * q^98 + 600 * q^99

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(2610))\)

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
2610.2.a	\(\chi_{2610}(1, \cdot)\)	2610.2.a.a	1	1
		2610.2.a.b	1
		2610.2.a.c	1
		2610.2.a.d	1
		2610.2.a.e	1
		2610.2.a.f	1
		2610.2.a.g	1
		2610.2.a.h	1
		2610.2.a.i	1
		2610.2.a.j	1
		2610.2.a.k	1
		2610.2.a.l	1
		2610.2.a.m	1
		2610.2.a.n	1
		2610.2.a.o	2
		2610.2.a.p	2
		2610.2.a.q	2
		2610.2.a.r	2
		2610.2.a.s	2
		2610.2.a.t	2
		2610.2.a.u	2
		2610.2.a.v	2
		2610.2.a.w	3
		2610.2.a.x	3
		2610.2.a.y	4
		2610.2.a.z	4
2610.2.b	\(\chi_{2610}(289, \cdot)\)	2610.2.b.a	6	1
		2610.2.b.b	6
		2610.2.b.c	8
		2610.2.b.d	8
		2610.2.b.e	8
		2610.2.b.f	8
		2610.2.b.g	16
		2610.2.b.h	16
2610.2.e	\(\chi_{2610}(2089, \cdot)\)	2610.2.e.a	2	1
		2610.2.e.b	2
		2610.2.e.c	2
		2610.2.e.d	2
		2610.2.e.e	4
		2610.2.e.f	4
		2610.2.e.g	6
		2610.2.e.h	10
		2610.2.e.i	10
		2610.2.e.j	14
		2610.2.e.k	14
2610.2.f	\(\chi_{2610}(811, \cdot)\)	2610.2.f.a	2	1
		2610.2.f.b	2
		2610.2.f.c	2
		2610.2.f.d	4
		2610.2.f.e	4
		2610.2.f.f	4
		2610.2.f.g	6
		2610.2.f.h	6
		2610.2.f.i	10
		2610.2.f.j	10
2610.2.i	\(\chi_{2610}(871, \cdot)\)	n/a	224	2
2610.2.k	\(\chi_{2610}(539, \cdot)\)	n/a	120	2
2610.2.l	\(\chi_{2610}(233, \cdot)\)	n/a	112	2
2610.2.o	\(\chi_{2610}(1027, \cdot)\)	n/a	150	2
2610.2.p	\(\chi_{2610}(307, \cdot)\)	n/a	150	2
2610.2.s	\(\chi_{2610}(1043, \cdot)\)	n/a	120	2
2610.2.t	\(\chi_{2610}(1061, \cdot)\)	2610.2.t.a	20	2
		2610.2.t.b	20
		2610.2.t.c	20
		2610.2.t.d	20
2610.2.w	\(\chi_{2610}(1681, \cdot)\)	n/a	240	2
2610.2.z	\(\chi_{2610}(349, \cdot)\)	n/a	336	2
2610.2.ba	\(\chi_{2610}(1159, \cdot)\)	n/a	360	2
2610.2.bc	\(\chi_{2610}(181, \cdot)\)	n/a	300	6
2610.2.be	\(\chi_{2610}(41, \cdot)\)	n/a	480	4
2610.2.bg	\(\chi_{2610}(173, \cdot)\)	n/a	720	4
2610.2.bi	\(\chi_{2610}(133, \cdot)\)	n/a	720	4
2610.2.bj	\(\chi_{2610}(853, \cdot)\)	n/a	720	4
2610.2.bl	\(\chi_{2610}(407, \cdot)\)	n/a	672	4
2610.2.bn	\(\chi_{2610}(389, \cdot)\)	n/a	720	4
2610.2.br	\(\chi_{2610}(91, \cdot)\)	n/a	300	6
2610.2.bs	\(\chi_{2610}(199, \cdot)\)	n/a	444	6
2610.2.bv	\(\chi_{2610}(109, \cdot)\)	n/a	456	6
2610.2.bw	\(\chi_{2610}(571, \cdot)\)	n/a	1440	12
2610.2.by	\(\chi_{2610}(251, \cdot)\)	n/a	480	12
2610.2.bz	\(\chi_{2610}(323, \cdot)\)	n/a	720	12
2610.2.cb	\(\chi_{2610}(37, \cdot)\)	n/a	900	12
2610.2.ce	\(\chi_{2610}(73, \cdot)\)	n/a	900	12
2610.2.cg	\(\chi_{2610}(53, \cdot)\)	n/a	720	12
2610.2.ch	\(\chi_{2610}(89, \cdot)\)	n/a	720	12
2610.2.ck	\(\chi_{2610}(439, \cdot)\)	n/a	2160	12
2610.2.cl	\(\chi_{2610}(49, \cdot)\)	n/a	2160	12
2610.2.co	\(\chi_{2610}(121, \cdot)\)	n/a	1440	12
2610.2.cr	\(\chi_{2610}(119, \cdot)\)	n/a	4320	24
2610.2.ct	\(\chi_{2610}(23, \cdot)\)	n/a	4320	24
2610.2.cu	\(\chi_{2610}(43, \cdot)\)	n/a	4320	24
2610.2.cx	\(\chi_{2610}(367, \cdot)\)	n/a	4320	24
2610.2.cy	\(\chi_{2610}(167, \cdot)\)	n/a	4320	24
2610.2.da	\(\chi_{2610}(11, \cdot)\)	n/a	2880	24

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(2610))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(2610)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(29))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(58))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(87))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(145))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(174))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(261))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(290))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(435))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(522))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(870))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1305))\)\(^{\oplus 2}\)