# Properties

 Label 8512.2 Level 8512 Weight 2 Dimension 1181956 Nonzero newspaces 128 Sturm bound 8847360

## Defining parameters

 Level: $$N$$ = $$8512 = 2^{6} \cdot 7 \cdot 19$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$128$$ Sturm bound: $$8847360$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8512))$$.

Total New Old
Modular forms 2227392 1189436 1037956
Cusp forms 2196289 1181956 1014333
Eisenstein series 31103 7480 23623

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8512))$$

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
8512.2.a $$\chi_{8512}(1, \cdot)$$ 8512.2.a.a 1 1
8512.2.a.b 1
8512.2.a.c 1
8512.2.a.d 1
8512.2.a.e 2
8512.2.a.f 2
8512.2.a.g 2
8512.2.a.h 2
8512.2.a.i 2
8512.2.a.j 2
8512.2.a.k 2
8512.2.a.l 2
8512.2.a.m 2
8512.2.a.n 2
8512.2.a.o 2
8512.2.a.p 2
8512.2.a.q 2
8512.2.a.r 2
8512.2.a.s 2
8512.2.a.t 2
8512.2.a.u 2
8512.2.a.v 2
8512.2.a.w 2
8512.2.a.x 2
8512.2.a.y 2
8512.2.a.z 2
8512.2.a.ba 2
8512.2.a.bb 2
8512.2.a.bc 2
8512.2.a.bd 2
8512.2.a.be 2
8512.2.a.bf 2
8512.2.a.bg 2
8512.2.a.bh 2
8512.2.a.bi 3
8512.2.a.bj 3
8512.2.a.bk 3
8512.2.a.bl 3
8512.2.a.bm 3
8512.2.a.bn 3
8512.2.a.bo 3
8512.2.a.bp 3
8512.2.a.bq 4
8512.2.a.br 4
8512.2.a.bs 4
8512.2.a.bt 4
8512.2.a.bu 4
8512.2.a.bv 4
8512.2.a.bw 5
8512.2.a.bx 5
8512.2.a.by 5
8512.2.a.bz 5
8512.2.a.ca 6
8512.2.a.cb 6
8512.2.a.cc 6
8512.2.a.cd 6
8512.2.a.ce 6
8512.2.a.cf 6
8512.2.a.cg 7
8512.2.a.ch 7
8512.2.a.ci 7
8512.2.a.cj 7
8512.2.a.ck 10
8512.2.a.cl 10
8512.2.b $$\chi_{8512}(4257, \cdot)$$ n/a 216 1
8512.2.e $$\chi_{8512}(3039, \cdot)$$ n/a 240 1
8512.2.f $$\chi_{8512}(7713, \cdot)$$ n/a 320 1
8512.2.i $$\chi_{8512}(2015, \cdot)$$ n/a 288 1
8512.2.j $$\chi_{8512}(6271, \cdot)$$ n/a 288 1
8512.2.m $$\chi_{8512}(3457, \cdot)$$ n/a 316 1
8512.2.n $$\chi_{8512}(7295, \cdot)$$ n/a 240 1
8512.2.q $$\chi_{8512}(2433, \cdot)$$ n/a 576 2
8512.2.r $$\chi_{8512}(1793, \cdot)$$ n/a 480 2
8512.2.s $$\chi_{8512}(5441, \cdot)$$ n/a 632 2
8512.2.t $$\chi_{8512}(961, \cdot)$$ n/a 632 2
8512.2.u $$\chi_{8512}(1329, \cdot)$$ n/a 632 2
8512.2.v $$\chi_{8512}(4143, \cdot)$$ n/a 576 2
8512.2.ba $$\chi_{8512}(2129, \cdot)$$ n/a 432 2
8512.2.bb $$\chi_{8512}(911, \cdot)$$ n/a 480 2
8512.2.bc $$\chi_{8512}(1375, \cdot)$$ n/a 640 2
8512.2.bf $$\chi_{8512}(3489, \cdot)$$ n/a 640 2
8512.2.bg $$\chi_{8512}(863, \cdot)$$ n/a 640 2
8512.2.bj $$\chi_{8512}(5217, \cdot)$$ n/a 640 2
8512.2.bk $$\chi_{8512}(3713, \cdot)$$ n/a 632 2
8512.2.bn $$\chi_{8512}(1151, \cdot)$$ n/a 632 2
8512.2.bp $$\chi_{8512}(1471, \cdot)$$ n/a 480 2
8512.2.br $$\chi_{8512}(1215, \cdot)$$ n/a 632 2
8512.2.bv $$\chi_{8512}(3583, \cdot)$$ n/a 632 2
8512.2.bx $$\chi_{8512}(1025, \cdot)$$ n/a 632 2
8512.2.by $$\chi_{8512}(2623, \cdot)$$ n/a 576 2
8512.2.ca $$\chi_{8512}(1665, \cdot)$$ n/a 632 2
8512.2.ce $$\chi_{8512}(639, \cdot)$$ n/a 632 2
8512.2.cf $$\chi_{8512}(4895, \cdot)$$ n/a 640 2
8512.2.ci $$\chi_{8512}(1185, \cdot)$$ n/a 640 2
8512.2.ck $$\chi_{8512}(1889, \cdot)$$ n/a 640 2
8512.2.cm $$\chi_{8512}(6879, \cdot)$$ n/a 576 2
8512.2.cn $$\chi_{8512}(4065, \cdot)$$ n/a 640 2
8512.2.cp $$\chi_{8512}(3807, \cdot)$$ n/a 640 2
8512.2.cs $$\chi_{8512}(1569, \cdot)$$ n/a 480 2
8512.2.cu $$\chi_{8512}(5471, \cdot)$$ n/a 640 2
8512.2.cv $$\chi_{8512}(6689, \cdot)$$ n/a 576 2
8512.2.cx $$\chi_{8512}(1247, \cdot)$$ n/a 480 2
8512.2.cz $$\chi_{8512}(159, \cdot)$$ n/a 640 2
8512.2.dc $$\chi_{8512}(2273, \cdot)$$ n/a 640 2
8512.2.df $$\chi_{8512}(5119, \cdot)$$ n/a 632 2
8512.2.dg $$\chi_{8512}(2497, \cdot)$$ n/a 632 2
8512.2.dj $$\chi_{8512}(5631, \cdot)$$ n/a 632 2
8512.2.dk $$\chi_{8512}(1975, \cdot)$$ None 0 4
8512.2.dl $$\chi_{8512}(1065, \cdot)$$ None 0 4
8512.2.dq $$\chi_{8512}(951, \cdot)$$ None 0 4
8512.2.dr $$\chi_{8512}(265, \cdot)$$ None 0 4
8512.2.ds $$\chi_{8512}(897, \cdot)$$ n/a 1440 6
8512.2.dt $$\chi_{8512}(1537, \cdot)$$ n/a 1896 6
8512.2.du $$\chi_{8512}(1089, \cdot)$$ n/a 1896 6
8512.2.dx $$\chi_{8512}(2097, \cdot)$$ n/a 1264 4
8512.2.dy $$\chi_{8512}(1551, \cdot)$$ n/a 1264 4
8512.2.dz $$\chi_{8512}(369, \cdot)$$ n/a 1264 4
8512.2.ea $$\chi_{8512}(2063, \cdot)$$ n/a 1264 4
8512.2.ef $$\chi_{8512}(495, \cdot)$$ n/a 1152 4
8512.2.eg $$\chi_{8512}(1937, \cdot)$$ n/a 1264 4
8512.2.eh $$\chi_{8512}(1775, \cdot)$$ n/a 1264 4
8512.2.ei $$\chi_{8512}(3375, \cdot)$$ n/a 960 4
8512.2.ej $$\chi_{8512}(1873, \cdot)$$ n/a 1264 4
8512.2.ek $$\chi_{8512}(3697, \cdot)$$ n/a 960 4
8512.2.et $$\chi_{8512}(2287, \cdot)$$ n/a 1264 4
8512.2.eu $$\chi_{8512}(1455, \cdot)$$ n/a 1264 4
8512.2.ev $$\chi_{8512}(145, \cdot)$$ n/a 1264 4
8512.2.ew $$\chi_{8512}(3793, \cdot)$$ n/a 1264 4
8512.2.ex $$\chi_{8512}(303, \cdot)$$ n/a 1264 4
8512.2.ey $$\chi_{8512}(305, \cdot)$$ n/a 1152 4
8512.2.fb $$\chi_{8512}(797, \cdot)$$ n/a 10208 8
8512.2.fc $$\chi_{8512}(533, \cdot)$$ n/a 6912 8
8512.2.fd $$\chi_{8512}(379, \cdot)$$ n/a 7680 8
8512.2.fe $$\chi_{8512}(419, \cdot)$$ n/a 9216 8
8512.2.fj $$\chi_{8512}(1727, \cdot)$$ n/a 1896 6
8512.2.fk $$\chi_{8512}(319, \cdot)$$ n/a 1896 6
8512.2.fn $$\chi_{8512}(33, \cdot)$$ n/a 1920 6
8512.2.fo $$\chi_{8512}(3425, \cdot)$$ n/a 1920 6
8512.2.ft $$\chi_{8512}(2561, \cdot)$$ n/a 1896 6
8512.2.fw $$\chi_{8512}(257, \cdot)$$ n/a 1896 6
8512.2.fz $$\chi_{8512}(671, \cdot)$$ n/a 1920 6
8512.2.ga $$\chi_{8512}(2143, \cdot)$$ n/a 1440 6
8512.2.gd $$\chi_{8512}(991, \cdot)$$ n/a 1920 6
8512.2.ge $$\chi_{8512}(3615, \cdot)$$ n/a 1920 6
8512.2.gh $$\chi_{8512}(127, \cdot)$$ n/a 1440 6
8512.2.gi $$\chi_{8512}(1791, \cdot)$$ n/a 1896 6
8512.2.gl $$\chi_{8512}(1279, \cdot)$$ n/a 1896 6
8512.2.gm $$\chi_{8512}(1535, \cdot)$$ n/a 1896 6
8512.2.gp $$\chi_{8512}(225, \cdot)$$ n/a 1440 6
8512.2.gq $$\chi_{8512}(97, \cdot)$$ n/a 1920 6
8512.2.gt $$\chi_{8512}(801, \cdot)$$ n/a 1920 6
8512.2.gu $$\chi_{8512}(289, \cdot)$$ n/a 1920 6
8512.2.gv $$\chi_{8512}(129, \cdot)$$ n/a 1896 6
8512.2.gy $$\chi_{8512}(2207, \cdot)$$ n/a 1920 6
8512.2.gz $$\chi_{8512}(479, \cdot)$$ n/a 1920 6
8512.2.he $$\chi_{8512}(457, \cdot)$$ None 0 8
8512.2.hf $$\chi_{8512}(151, \cdot)$$ None 0 8
8512.2.hi $$\chi_{8512}(87, \cdot)$$ None 0 8
8512.2.hj $$\chi_{8512}(521, \cdot)$$ None 0 8
8512.2.hk $$\chi_{8512}(601, \cdot)$$ None 0 8
8512.2.hl $$\chi_{8512}(391, \cdot)$$ None 0 8
8512.2.hq $$\chi_{8512}(297, \cdot)$$ None 0 8
8512.2.hr $$\chi_{8512}(311, \cdot)$$ None 0 8
8512.2.hs $$\chi_{8512}(1033, \cdot)$$ None 0 8
8512.2.ht $$\chi_{8512}(487, \cdot)$$ None 0 8
8512.2.hy $$\chi_{8512}(711, \cdot)$$ None 0 8
8512.2.hz $$\chi_{8512}(121, \cdot)$$ None 0 8
8512.2.ia $$\chi_{8512}(505, \cdot)$$ None 0 8
8512.2.ib $$\chi_{8512}(183, \cdot)$$ None 0 8
8512.2.ie $$\chi_{8512}(873, \cdot)$$ None 0 8
8512.2.if $$\chi_{8512}(647, \cdot)$$ None 0 8
8512.2.im $$\chi_{8512}(785, \cdot)$$ n/a 2880 12
8512.2.in $$\chi_{8512}(433, \cdot)$$ n/a 3792 12
8512.2.io $$\chi_{8512}(271, \cdot)$$ n/a 3792 12
8512.2.ip $$\chi_{8512}(79, \cdot)$$ n/a 3792 12
8512.2.iq $$\chi_{8512}(625, \cdot)$$ n/a 3792 12
8512.2.ir $$\chi_{8512}(241, \cdot)$$ n/a 3792 12
8512.2.is $$\chi_{8512}(111, \cdot)$$ n/a 3792 12
8512.2.it $$\chi_{8512}(15, \cdot)$$ n/a 2880 12
8512.2.jc $$\chi_{8512}(751, \cdot)$$ n/a 3792 12
8512.2.jd $$\chi_{8512}(47, \cdot)$$ n/a 3792 12
8512.2.je $$\chi_{8512}(1041, \cdot)$$ n/a 3792 12
8512.2.jf $$\chi_{8512}(81, \cdot)$$ n/a 3792 12
8512.2.jg $$\chi_{8512}(715, \cdot)$$ n/a 15360 16
8512.2.jh $$\chi_{8512}(83, \cdot)$$ n/a 20416 16
8512.2.ji $$\chi_{8512}(69, \cdot)$$ n/a 20416 16
8512.2.jj $$\chi_{8512}(197, \cdot)$$ n/a 15360 16
8512.2.jw $$\chi_{8512}(277, \cdot)$$ n/a 20416 16
8512.2.jx $$\chi_{8512}(677, \cdot)$$ n/a 20416 16
8512.2.jy $$\chi_{8512}(467, \cdot)$$ n/a 20416 16
8512.2.jz $$\chi_{8512}(115, \cdot)$$ n/a 18432 16
8512.2.ka $$\chi_{8512}(331, \cdot)$$ n/a 20416 16
8512.2.kb $$\chi_{8512}(683, \cdot)$$ n/a 20416 16
8512.2.kc $$\chi_{8512}(837, \cdot)$$ n/a 18432 16
8512.2.kd $$\chi_{8512}(429, \cdot)$$ n/a 20416 16
8512.2.ke $$\chi_{8512}(341, \cdot)$$ n/a 20416 16
8512.2.kf $$\chi_{8512}(829, \cdot)$$ n/a 20416 16
8512.2.kg $$\chi_{8512}(619, \cdot)$$ n/a 20416 16
8512.2.kh $$\chi_{8512}(107, \cdot)$$ n/a 20416 16
8512.2.kq $$\chi_{8512}(25, \cdot)$$ None 0 24
8512.2.kr $$\chi_{8512}(55, \cdot)$$ None 0 24
8512.2.ks $$\chi_{8512}(169, \cdot)$$ None 0 24
8512.2.kt $$\chi_{8512}(199, \cdot)$$ None 0 24
8512.2.ku $$\chi_{8512}(409, \cdot)$$ None 0 24
8512.2.kv $$\chi_{8512}(71, \cdot)$$ None 0 24
8512.2.kw $$\chi_{8512}(41, \cdot)$$ None 0 24
8512.2.kx $$\chi_{8512}(135, \cdot)$$ None 0 24
8512.2.lg $$\chi_{8512}(375, \cdot)$$ None 0 24
8512.2.lh $$\chi_{8512}(89, \cdot)$$ None 0 24
8512.2.li $$\chi_{8512}(215, \cdot)$$ None 0 24
8512.2.lj $$\chi_{8512}(9, \cdot)$$ None 0 24
8512.2.lk $$\chi_{8512}(269, \cdot)$$ n/a 61248 48
8512.2.ll $$\chi_{8512}(51, \cdot)$$ n/a 61248 48
8512.2.lm $$\chi_{8512}(541, \cdot)$$ n/a 61248 48
8512.2.ln $$\chi_{8512}(283, \cdot)$$ n/a 61248 48
8512.2.lw $$\chi_{8512}(93, \cdot)$$ n/a 61248 48
8512.2.lx $$\chi_{8512}(131, \cdot)$$ n/a 61248 48
8512.2.ly $$\chi_{8512}(139, \cdot)$$ n/a 61248 48
8512.2.lz $$\chi_{8512}(85, \cdot)$$ n/a 46080 48
8512.2.ma $$\chi_{8512}(155, \cdot)$$ n/a 46080 48
8512.2.mb $$\chi_{8512}(13, \cdot)$$ n/a 61248 48
8512.2.mc $$\chi_{8512}(117, \cdot)$$ n/a 61248 48
8512.2.md $$\chi_{8512}(67, \cdot)$$ n/a 61248 48

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8512))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8512)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 28}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(7))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(19))$$$$^{\oplus 14}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(32))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(38))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(64))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(76))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(112))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(133))$$$$^{\oplus 7}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(152))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(224))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(266))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(304))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(448))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(532))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(608))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1064))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1216))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2128))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4256))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8512))$$$$^{\oplus 1}$$