# Properties

 Label 5850.2 Level 5850 Weight 2 Dimension 218021 Nonzero newspaces 100 Sturm bound 3628800

## Defining parameters

 Level: $$N$$ = $$5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$100$$ Sturm bound: $$3628800$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5850))$$.

Total New Old
Modular forms 917952 218021 699931
Cusp forms 896449 218021 678428
Eisenstein series 21503 0 21503

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5850))$$

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
5850.2.a $$\chi_{5850}(1, \cdot)$$ 5850.2.a.a 1 1
5850.2.a.b 1
5850.2.a.c 1
5850.2.a.d 1
5850.2.a.e 1
5850.2.a.f 1
5850.2.a.g 1
5850.2.a.h 1
5850.2.a.i 1
5850.2.a.j 1
5850.2.a.k 1
5850.2.a.l 1
5850.2.a.m 1
5850.2.a.n 1
5850.2.a.o 1
5850.2.a.p 1
5850.2.a.q 1
5850.2.a.r 1
5850.2.a.s 1
5850.2.a.t 1
5850.2.a.u 1
5850.2.a.v 1
5850.2.a.w 1
5850.2.a.x 1
5850.2.a.y 1
5850.2.a.z 1
5850.2.a.ba 1
5850.2.a.bb 1
5850.2.a.bc 1
5850.2.a.bd 1
5850.2.a.be 1
5850.2.a.bf 1
5850.2.a.bg 1
5850.2.a.bh 1
5850.2.a.bi 1
5850.2.a.bj 1
5850.2.a.bk 1
5850.2.a.bl 1
5850.2.a.bm 1
5850.2.a.bn 1
5850.2.a.bo 1
5850.2.a.bp 1
5850.2.a.bq 1
5850.2.a.br 1
5850.2.a.bs 1
5850.2.a.bt 1
5850.2.a.bu 1
5850.2.a.bv 1
5850.2.a.bw 1
5850.2.a.bx 1
5850.2.a.by 1
5850.2.a.bz 1
5850.2.a.ca 1
5850.2.a.cb 1
5850.2.a.cc 1
5850.2.a.cd 2
5850.2.a.ce 2
5850.2.a.cf 2
5850.2.a.cg 2
5850.2.a.ch 2
5850.2.a.ci 2
5850.2.a.cj 2
5850.2.a.ck 2
5850.2.a.cl 2
5850.2.a.cm 2
5850.2.a.cn 2
5850.2.a.co 3
5850.2.a.cp 3
5850.2.a.cq 3
5850.2.a.cr 3
5850.2.a.cs 3
5850.2.a.ct 3
5850.2.b $$\chi_{5850}(1351, \cdot)$$ n/a 110 1
5850.2.e $$\chi_{5850}(5149, \cdot)$$ 5850.2.e.a 2 1
5850.2.e.b 2
5850.2.e.c 2
5850.2.e.d 2
5850.2.e.e 2
5850.2.e.f 2
5850.2.e.g 2
5850.2.e.h 2
5850.2.e.i 2
5850.2.e.j 2
5850.2.e.k 2
5850.2.e.l 2
5850.2.e.m 2
5850.2.e.n 2
5850.2.e.o 2
5850.2.e.p 2
5850.2.e.q 2
5850.2.e.r 2
5850.2.e.s 2
5850.2.e.t 2
5850.2.e.u 2
5850.2.e.v 2
5850.2.e.w 2
5850.2.e.x 2
5850.2.e.y 2
5850.2.e.z 2
5850.2.e.ba 2
5850.2.e.bb 2
5850.2.e.bc 2
5850.2.e.bd 2
5850.2.e.be 2
5850.2.e.bf 2
5850.2.e.bg 2
5850.2.e.bh 4
5850.2.e.bi 4
5850.2.e.bj 4
5850.2.e.bk 4
5850.2.e.bl 4
5850.2.e.bm 4
5850.2.f $$\chi_{5850}(649, \cdot)$$ n/a 104 1
5850.2.i $$\chi_{5850}(451, \cdot)$$ n/a 222 2
5850.2.j $$\chi_{5850}(1951, \cdot)$$ n/a 456 2
5850.2.k $$\chi_{5850}(601, \cdot)$$ n/a 532 2
5850.2.l $$\chi_{5850}(2401, \cdot)$$ n/a 532 2
5850.2.m $$\chi_{5850}(1243, \cdot)$$ n/a 210 2
5850.2.o $$\chi_{5850}(1457, \cdot)$$ n/a 144 2
5850.2.q $$\chi_{5850}(1799, \cdot)$$ n/a 168 2
5850.2.s $$\chi_{5850}(2501, \cdot)$$ n/a 172 2
5850.2.v $$\chi_{5850}(2807, \cdot)$$ n/a 168 2
5850.2.w $$\chi_{5850}(307, \cdot)$$ n/a 210 2
5850.2.y $$\chi_{5850}(1171, \cdot)$$ n/a 600 4
5850.2.z $$\chi_{5850}(1699, \cdot)$$ n/a 504 2
5850.2.bc $$\chi_{5850}(751, \cdot)$$ n/a 532 2
5850.2.be $$\chi_{5850}(3949, \cdot)$$ n/a 504 2
5850.2.bh $$\chi_{5850}(2599, \cdot)$$ n/a 504 2
5850.2.bk $$\chi_{5850}(199, \cdot)$$ n/a 208 2
5850.2.bn $$\chi_{5850}(4651, \cdot)$$ n/a 532 2
5850.2.bp $$\chi_{5850}(1249, \cdot)$$ n/a 432 2
5850.2.bq $$\chi_{5850}(3799, \cdot)$$ n/a 212 2
5850.2.bt $$\chi_{5850}(901, \cdot)$$ n/a 224 2
5850.2.bu $$\chi_{5850}(3301, \cdot)$$ n/a 532 2
5850.2.bw $$\chi_{5850}(3649, \cdot)$$ n/a 504 2
5850.2.ca $$\chi_{5850}(49, \cdot)$$ n/a 504 2
5850.2.cb $$\chi_{5850}(469, \cdot)$$ n/a 600 4
5850.2.ce $$\chi_{5850}(181, \cdot)$$ n/a 696 4
5850.2.ch $$\chi_{5850}(1819, \cdot)$$ n/a 704 4
5850.2.cj $$\chi_{5850}(193, \cdot)$$ n/a 1008 4
5850.2.ck $$\chi_{5850}(643, \cdot)$$ n/a 1008 4
5850.2.cn $$\chi_{5850}(1207, \cdot)$$ n/a 420 4
5850.2.co $$\chi_{5850}(2257, \cdot)$$ n/a 1008 4
5850.2.cr $$\chi_{5850}(3857, \cdot)$$ n/a 1008 4
5850.2.ct $$\chi_{5850}(2357, \cdot)$$ n/a 336 4
5850.2.cu $$\chi_{5850}(257, \cdot)$$ n/a 1008 4
5850.2.cx $$\chi_{5850}(857, \cdot)$$ n/a 1008 4
5850.2.cz $$\chi_{5850}(749, \cdot)$$ n/a 1008 4
5850.2.da $$\chi_{5850}(851, \cdot)$$ n/a 1064 4
5850.2.dc $$\chi_{5850}(1151, \cdot)$$ n/a 360 4
5850.2.df $$\chi_{5850}(401, \cdot)$$ n/a 1064 4
5850.2.dh $$\chi_{5850}(2099, \cdot)$$ n/a 1008 4
5850.2.di $$\chi_{5850}(149, \cdot)$$ n/a 1008 4
5850.2.dk $$\chi_{5850}(449, \cdot)$$ n/a 336 4
5850.2.dn $$\chi_{5850}(551, \cdot)$$ n/a 1064 4
5850.2.do $$\chi_{5850}(443, \cdot)$$ n/a 864 4
5850.2.dr $$\chi_{5850}(893, \cdot)$$ n/a 1008 4
5850.2.ds $$\chi_{5850}(107, \cdot)$$ n/a 336 4
5850.2.du $$\chi_{5850}(2207, \cdot)$$ n/a 1008 4
5850.2.dw $$\chi_{5850}(457, \cdot)$$ n/a 1008 4
5850.2.dz $$\chi_{5850}(1357, \cdot)$$ n/a 1008 4
5850.2.ea $$\chi_{5850}(1657, \cdot)$$ n/a 420 4
5850.2.ed $$\chi_{5850}(7, \cdot)$$ n/a 1008 4
5850.2.ee $$\chi_{5850}(841, \cdot)$$ n/a 3360 8
5850.2.ef $$\chi_{5850}(391, \cdot)$$ n/a 2880 8
5850.2.eg $$\chi_{5850}(991, \cdot)$$ n/a 1408 8
5850.2.eh $$\chi_{5850}(61, \cdot)$$ n/a 3360 8
5850.2.ej $$\chi_{5850}(73, \cdot)$$ n/a 1400 8
5850.2.ek $$\chi_{5850}(233, \cdot)$$ n/a 1120 8
5850.2.en $$\chi_{5850}(161, \cdot)$$ n/a 1120 8
5850.2.ep $$\chi_{5850}(359, \cdot)$$ n/a 1120 8
5850.2.er $$\chi_{5850}(53, \cdot)$$ n/a 960 8
5850.2.et $$\chi_{5850}(1477, \cdot)$$ n/a 1400 8
5850.2.eu $$\chi_{5850}(511, \cdot)$$ n/a 3360 8
5850.2.ex $$\chi_{5850}(529, \cdot)$$ n/a 3360 8
5850.2.ez $$\chi_{5850}(829, \cdot)$$ n/a 1408 8
5850.2.fc $$\chi_{5850}(259, \cdot)$$ n/a 3360 8
5850.2.ff $$\chi_{5850}(439, \cdot)$$ n/a 3360 8
5850.2.fi $$\chi_{5850}(139, \cdot)$$ n/a 3360 8
5850.2.fk $$\chi_{5850}(571, \cdot)$$ n/a 3360 8
5850.2.fl $$\chi_{5850}(361, \cdot)$$ n/a 1392 8
5850.2.fo $$\chi_{5850}(289, \cdot)$$ n/a 1392 8
5850.2.fp $$\chi_{5850}(79, \cdot)$$ n/a 2880 8
5850.2.fr $$\chi_{5850}(121, \cdot)$$ n/a 3360 8
5850.2.ft $$\chi_{5850}(979, \cdot)$$ n/a 3360 8
5850.2.fw $$\chi_{5850}(67, \cdot)$$ n/a 6720 16
5850.2.fz $$\chi_{5850}(697, \cdot)$$ n/a 6720 16
5850.2.ga $$\chi_{5850}(37, \cdot)$$ n/a 2800 16
5850.2.gd $$\chi_{5850}(223, \cdot)$$ n/a 6720 16
5850.2.gf $$\chi_{5850}(563, \cdot)$$ n/a 6720 16
5850.2.gh $$\chi_{5850}(503, \cdot)$$ n/a 2240 16
5850.2.gi $$\chi_{5850}(653, \cdot)$$ n/a 6720 16
5850.2.gl $$\chi_{5850}(677, \cdot)$$ n/a 5760 16
5850.2.gm $$\chi_{5850}(281, \cdot)$$ n/a 6720 16
5850.2.gp $$\chi_{5850}(89, \cdot)$$ n/a 2240 16
5850.2.gr $$\chi_{5850}(59, \cdot)$$ n/a 6720 16
5850.2.gs $$\chi_{5850}(509, \cdot)$$ n/a 6720 16
5850.2.gu $$\chi_{5850}(41, \cdot)$$ n/a 6720 16
5850.2.gx $$\chi_{5850}(71, \cdot)$$ n/a 2240 16
5850.2.gz $$\chi_{5850}(11, \cdot)$$ n/a 6720 16
5850.2.ha $$\chi_{5850}(239, \cdot)$$ n/a 6720 16
5850.2.hc $$\chi_{5850}(77, \cdot)$$ n/a 6720 16
5850.2.hf $$\chi_{5850}(23, \cdot)$$ n/a 6720 16
5850.2.hg $$\chi_{5850}(17, \cdot)$$ n/a 2240 16
5850.2.hi $$\chi_{5850}(113, \cdot)$$ n/a 6720 16
5850.2.hl $$\chi_{5850}(163, \cdot)$$ n/a 2800 16
5850.2.hm $$\chi_{5850}(187, \cdot)$$ n/a 6720 16
5850.2.hp $$\chi_{5850}(553, \cdot)$$ n/a 6720 16
5850.2.hq $$\chi_{5850}(427, \cdot)$$ n/a 6720 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5850))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5850)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 36}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(6))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(18))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(45))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(90))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(117))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(225))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(234))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(450))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(585))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(650))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(975))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1170))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1950))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2925))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5850))$$$$^{\oplus 1}$$