# Properties

 Label 5610.2 Level 5610 Weight 2 Dimension 185623 Nonzero newspaces 72 Sturm bound 3317760

## Defining parameters

 Level: $$N$$ = $$5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$72$$ Sturm bound: $$3317760$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5610))$$.

Total New Old
Modular forms 839680 185623 654057
Cusp forms 819201 185623 633578
Eisenstein series 20479 0 20479

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5610))$$

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 the newforms together with their dimension.

Label $$\chi$$ Newforms Dimension $$\chi$$ degree
5610.2.a $$\chi_{5610}(1, \cdot)$$ 5610.2.a.a 1 1
5610.2.a.b 1
5610.2.a.c 1
5610.2.a.d 1
5610.2.a.e 1
5610.2.a.f 1
5610.2.a.g 1
5610.2.a.h 1
5610.2.a.i 1
5610.2.a.j 1
5610.2.a.k 1
5610.2.a.l 1
5610.2.a.m 1
5610.2.a.n 1
5610.2.a.o 1
5610.2.a.p 1
5610.2.a.q 1
5610.2.a.r 1
5610.2.a.s 1
5610.2.a.t 1
5610.2.a.u 1
5610.2.a.v 1
5610.2.a.w 1
5610.2.a.x 1
5610.2.a.y 1
5610.2.a.z 1
5610.2.a.ba 1
5610.2.a.bb 1
5610.2.a.bc 1
5610.2.a.bd 1
5610.2.a.be 1
5610.2.a.bf 1
5610.2.a.bg 1
5610.2.a.bh 1
5610.2.a.bi 1
5610.2.a.bj 1
5610.2.a.bk 1
5610.2.a.bl 1
5610.2.a.bm 2
5610.2.a.bn 2
5610.2.a.bo 2
5610.2.a.bp 2
5610.2.a.bq 2
5610.2.a.br 2
5610.2.a.bs 2
5610.2.a.bt 2
5610.2.a.bu 2
5610.2.a.bv 2
5610.2.a.bw 2
5610.2.a.bx 2
5610.2.a.by 3
5610.2.a.bz 3
5610.2.a.ca 3
5610.2.a.cb 3
5610.2.a.cc 3
5610.2.a.cd 3
5610.2.a.ce 4
5610.2.a.cf 4
5610.2.a.cg 4
5610.2.a.ch 4
5610.2.a.ci 5
5610.2.a.cj 5
5610.2.a.ck 5
5610.2.b $$\chi_{5610}(4421, \cdot)$$ n/a 256 1
5610.2.d $$\chi_{5610}(4489, \cdot)$$ n/a 160 1
5610.2.f $$\chi_{5610}(5609, \cdot)$$ n/a 432 1
5610.2.h $$\chi_{5610}(2311, \cdot)$$ n/a 120 1
5610.2.k $$\chi_{5610}(1121, \cdot)$$ n/a 288 1
5610.2.m $$\chi_{5610}(1189, \cdot)$$ n/a 176 1
5610.2.o $$\chi_{5610}(3299, \cdot)$$ n/a 384 1
5610.2.q $$\chi_{5610}(3013, \cdot)$$ n/a 432 2
5610.2.s $$\chi_{5610}(353, \cdot)$$ n/a 720 2
5610.2.u $$\chi_{5610}(1849, \cdot)$$ n/a 352 2
5610.2.w $$\chi_{5610}(1781, \cdot)$$ n/a 576 2
5610.2.y $$\chi_{5610}(1937, \cdot)$$ n/a 720 2
5610.2.bb $$\chi_{5610}(2993, \cdot)$$ n/a 640 2
5610.2.bc $$\chi_{5610}(373, \cdot)$$ n/a 432 2
5610.2.bf $$\chi_{5610}(307, \cdot)$$ n/a 384 2
5610.2.bh $$\chi_{5610}(2971, \cdot)$$ n/a 240 2
5610.2.bj $$\chi_{5610}(659, \cdot)$$ n/a 864 2
5610.2.bl $$\chi_{5610}(1033, \cdot)$$ n/a 432 2
5610.2.bn $$\chi_{5610}(2333, \cdot)$$ n/a 720 2
5610.2.bo $$\chi_{5610}(511, \cdot)$$ n/a 512 4
5610.2.bp $$\chi_{5610}(3629, \cdot)$$ n/a 1728 4
5610.2.bq $$\chi_{5610}(331, \cdot)$$ n/a 480 4
5610.2.bt $$\chi_{5610}(287, \cdot)$$ n/a 1440 4
5610.2.bu $$\chi_{5610}(637, \cdot)$$ n/a 864 4
5610.2.bz $$\chi_{5610}(43, \cdot)$$ n/a 864 4
5610.2.ca $$\chi_{5610}(1607, \cdot)$$ n/a 1440 4
5610.2.cd $$\chi_{5610}(529, \cdot)$$ n/a 736 4
5610.2.ce $$\chi_{5610}(461, \cdot)$$ n/a 1152 4
5610.2.ch $$\chi_{5610}(239, \cdot)$$ n/a 1536 4
5610.2.cj $$\chi_{5610}(169, \cdot)$$ n/a 864 4
5610.2.cl $$\chi_{5610}(101, \cdot)$$ n/a 1152 4
5610.2.cm $$\chi_{5610}(1291, \cdot)$$ n/a 576 4
5610.2.co $$\chi_{5610}(1019, \cdot)$$ n/a 1728 4
5610.2.cq $$\chi_{5610}(1939, \cdot)$$ n/a 768 4
5610.2.cs $$\chi_{5610}(1361, \cdot)$$ n/a 1024 4
5610.2.cw $$\chi_{5610}(133, \cdot)$$ n/a 1440 8
5610.2.cx $$\chi_{5610}(1187, \cdot)$$ n/a 3456 8
5610.2.da $$\chi_{5610}(551, \cdot)$$ n/a 1920 8
5610.2.db $$\chi_{5610}(241, \cdot)$$ n/a 1152 8
5610.2.de $$\chi_{5610}(109, \cdot)$$ n/a 1728 8
5610.2.df $$\chi_{5610}(419, \cdot)$$ n/a 2880 8
5610.2.dg $$\chi_{5610}(197, \cdot)$$ n/a 3456 8
5610.2.dh $$\chi_{5610}(793, \cdot)$$ n/a 1440 8
5610.2.dl $$\chi_{5610}(47, \cdot)$$ n/a 3456 8
5610.2.dn $$\chi_{5610}(13, \cdot)$$ n/a 1728 8
5610.2.do $$\chi_{5610}(149, \cdot)$$ n/a 3456 8
5610.2.dq $$\chi_{5610}(361, \cdot)$$ n/a 1152 8
5610.2.ds $$\chi_{5610}(613, \cdot)$$ n/a 1536 8
5610.2.dv $$\chi_{5610}(1393, \cdot)$$ n/a 1728 8
5610.2.dw $$\chi_{5610}(137, \cdot)$$ n/a 3072 8
5610.2.dz $$\chi_{5610}(203, \cdot)$$ n/a 3456 8
5610.2.eb $$\chi_{5610}(701, \cdot)$$ n/a 2304 8
5610.2.ed $$\chi_{5610}(829, \cdot)$$ n/a 1728 8
5610.2.ee $$\chi_{5610}(863, \cdot)$$ n/a 3456 8
5610.2.eg $$\chi_{5610}(217, \cdot)$$ n/a 1728 8
5610.2.ei $$\chi_{5610}(49, \cdot)$$ n/a 3456 16
5610.2.ej $$\chi_{5610}(161, \cdot)$$ n/a 4608 16
5610.2.eo $$\chi_{5610}(127, \cdot)$$ n/a 3456 16
5610.2.ep $$\chi_{5610}(257, \cdot)$$ n/a 6912 16
5610.2.eq $$\chi_{5610}(53, \cdot)$$ n/a 6912 16
5610.2.er $$\chi_{5610}(457, \cdot)$$ n/a 3456 16
5610.2.ew $$\chi_{5610}(359, \cdot)$$ n/a 6912 16
5610.2.ex $$\chi_{5610}(631, \cdot)$$ n/a 2304 16
5610.2.fa $$\chi_{5610}(37, \cdot)$$ n/a 6912 32
5610.2.fb $$\chi_{5610}(173, \cdot)$$ n/a 13824 32
5610.2.fc $$\chi_{5610}(61, \cdot)$$ n/a 4608 32
5610.2.fd $$\chi_{5610}(71, \cdot)$$ n/a 9216 32
5610.2.fg $$\chi_{5610}(269, \cdot)$$ n/a 13824 32
5610.2.fh $$\chi_{5610}(79, \cdot)$$ n/a 6912 32
5610.2.fk $$\chi_{5610}(107, \cdot)$$ n/a 13824 32
5610.2.fl $$\chi_{5610}(367, \cdot)$$ n/a 6912 32

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5610))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5610)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(34))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(66))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(85))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(102))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(170))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(187))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(255))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(330))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(374))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(510))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(561))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(935))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1122))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1870))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2805))$$$$^{\oplus 2}$$