# Properties

 Label 8085.2 Level 8085 Weight 2 Dimension 1459560 Nonzero newspaces 96 Sturm bound 9031680

## Defining parameters

 Level: $$N$$ = $$8085 = 3 \cdot 5 \cdot 7^{2} \cdot 11$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$96$$ Sturm bound: $$9031680$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8085))$$.

Total New Old
Modular forms 2277120 1470032 807088
Cusp forms 2238721 1459560 779161
Eisenstein series 38399 10472 27927

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8085))$$

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
8085.2.a $$\chi_{8085}(1, \cdot)$$ 8085.2.a.a 1 1
8085.2.a.b 1
8085.2.a.c 1
8085.2.a.d 1
8085.2.a.e 1
8085.2.a.f 1
8085.2.a.g 1
8085.2.a.h 1
8085.2.a.i 1
8085.2.a.j 1
8085.2.a.k 1
8085.2.a.l 1
8085.2.a.m 1
8085.2.a.n 1
8085.2.a.o 1
8085.2.a.p 1
8085.2.a.q 1
8085.2.a.r 1
8085.2.a.s 1
8085.2.a.t 1
8085.2.a.u 1
8085.2.a.v 1
8085.2.a.w 1
8085.2.a.x 1
8085.2.a.y 1
8085.2.a.z 1
8085.2.a.ba 2
8085.2.a.bb 2
8085.2.a.bc 2
8085.2.a.bd 2
8085.2.a.be 2
8085.2.a.bf 2
8085.2.a.bg 2
8085.2.a.bh 2
8085.2.a.bi 3
8085.2.a.bj 3
8085.2.a.bk 3
8085.2.a.bl 3
8085.2.a.bm 3
8085.2.a.bn 4
8085.2.a.bo 4
8085.2.a.bp 4
8085.2.a.bq 4
8085.2.a.br 5
8085.2.a.bs 5
8085.2.a.bt 5
8085.2.a.bu 5
8085.2.a.bv 5
8085.2.a.bw 6
8085.2.a.bx 6
8085.2.a.by 6
8085.2.a.bz 6
8085.2.a.ca 7
8085.2.a.cb 7
8085.2.a.cc 7
8085.2.a.cd 7
8085.2.a.ce 8
8085.2.a.cf 8
8085.2.a.cg 9
8085.2.a.ch 9
8085.2.a.ci 10
8085.2.a.cj 10
8085.2.a.ck 10
8085.2.a.cl 10
8085.2.a.cm 10
8085.2.a.cn 10
8085.2.a.co 14
8085.2.a.cp 14
8085.2.c $$\chi_{8085}(6469, \cdot)$$ n/a 412 1
8085.2.d $$\chi_{8085}(881, \cdot)$$ n/a 536 1
8085.2.f $$\chi_{8085}(1814, \cdot)$$ n/a 964 1
8085.2.i $$\chi_{8085}(7006, \cdot)$$ n/a 320 1
8085.2.k $$\chi_{8085}(5389, \cdot)$$ n/a 480 1
8085.2.l $$\chi_{8085}(3431, \cdot)$$ n/a 656 1
8085.2.n $$\chi_{8085}(7349, \cdot)$$ n/a 800 1
8085.2.q $$\chi_{8085}(3301, \cdot)$$ n/a 536 2
8085.2.s $$\chi_{8085}(4313, \cdot)$$ n/a 1640 2
8085.2.t $$\chi_{8085}(3233, \cdot)$$ n/a 1888 2
8085.2.v $$\chi_{8085}(3037, \cdot)$$ n/a 800 2
8085.2.y $$\chi_{8085}(2353, \cdot)$$ n/a 984 2
8085.2.z $$\chi_{8085}(2941, \cdot)$$ n/a 1312 4
8085.2.bb $$\chi_{8085}(1451, \cdot)$$ n/a 1280 2
8085.2.bc $$\chi_{8085}(2089, \cdot)$$ n/a 960 2
8085.2.bg $$\chi_{8085}(1244, \cdot)$$ n/a 1600 2
8085.2.bi $$\chi_{8085}(2861, \cdot)$$ n/a 1064 2
8085.2.bj $$\chi_{8085}(1684, \cdot)$$ n/a 800 2
8085.2.bl $$\chi_{8085}(901, \cdot)$$ n/a 640 2
8085.2.bo $$\chi_{8085}(5114, \cdot)$$ n/a 1888 2
8085.2.bp $$\chi_{8085}(1156, \cdot)$$ n/a 2256 6
8085.2.bs $$\chi_{8085}(2204, \cdot)$$ n/a 3776 4
8085.2.bu $$\chi_{8085}(491, \cdot)$$ n/a 2624 4
8085.2.bv $$\chi_{8085}(244, \cdot)$$ n/a 1920 4
8085.2.bx $$\chi_{8085}(391, \cdot)$$ n/a 1280 4
8085.2.ca $$\chi_{8085}(2549, \cdot)$$ n/a 3856 4
8085.2.cc $$\chi_{8085}(146, \cdot)$$ n/a 2560 4
8085.2.cd $$\chi_{8085}(1324, \cdot)$$ n/a 1968 4
8085.2.cf $$\chi_{8085}(373, \cdot)$$ n/a 1920 4
8085.2.ci $$\chi_{8085}(1783, \cdot)$$ n/a 1600 4
8085.2.ck $$\chi_{8085}(362, \cdot)$$ n/a 3776 4
8085.2.cl $$\chi_{8085}(2333, \cdot)$$ n/a 3200 4
8085.2.co $$\chi_{8085}(419, \cdot)$$ n/a 6720 6
8085.2.cq $$\chi_{8085}(1121, \cdot)$$ n/a 5376 6
8085.2.ct $$\chi_{8085}(769, \cdot)$$ n/a 4032 6
8085.2.cv $$\chi_{8085}(76, \cdot)$$ n/a 2688 6
8085.2.cw $$\chi_{8085}(659, \cdot)$$ n/a 8016 6
8085.2.cy $$\chi_{8085}(2036, \cdot)$$ n/a 4464 6
8085.2.db $$\chi_{8085}(694, \cdot)$$ n/a 3360 6
8085.2.dc $$\chi_{8085}(361, \cdot)$$ n/a 2560 8
8085.2.dd $$\chi_{8085}(442, \cdot)$$ n/a 3936 8
8085.2.dg $$\chi_{8085}(97, \cdot)$$ n/a 3840 8
8085.2.di $$\chi_{8085}(293, \cdot)$$ n/a 7552 8
8085.2.dj $$\chi_{8085}(1373, \cdot)$$ n/a 7712 8
8085.2.dl $$\chi_{8085}(331, \cdot)$$ n/a 4464 12
8085.2.dm $$\chi_{8085}(692, \cdot)$$ n/a 16032 12
8085.2.dp $$\chi_{8085}(617, \cdot)$$ n/a 13440 12
8085.2.dr $$\chi_{8085}(43, \cdot)$$ n/a 8064 12
8085.2.ds $$\chi_{8085}(727, \cdot)$$ n/a 6720 12
8085.2.du $$\chi_{8085}(569, \cdot)$$ n/a 7552 8
8085.2.dx $$\chi_{8085}(766, \cdot)$$ n/a 2560 8
8085.2.dz $$\chi_{8085}(214, \cdot)$$ n/a 3840 8
8085.2.ea $$\chi_{8085}(521, \cdot)$$ n/a 5120 8
8085.2.ec $$\chi_{8085}(509, \cdot)$$ n/a 7552 8
8085.2.eg $$\chi_{8085}(19, \cdot)$$ n/a 3840 8
8085.2.eh $$\chi_{8085}(116, \cdot)$$ n/a 5120 8
8085.2.ej $$\chi_{8085}(421, \cdot)$$ n/a 10752 24
8085.2.el $$\chi_{8085}(494, \cdot)$$ n/a 16032 12
8085.2.em $$\chi_{8085}(241, \cdot)$$ n/a 5376 12
8085.2.eo $$\chi_{8085}(529, \cdot)$$ n/a 6720 12
8085.2.er $$\chi_{8085}(551, \cdot)$$ n/a 8976 12
8085.2.et $$\chi_{8085}(89, \cdot)$$ n/a 13440 12
8085.2.ev $$\chi_{8085}(439, \cdot)$$ n/a 8064 12
8085.2.ey $$\chi_{8085}(296, \cdot)$$ n/a 10752 12
8085.2.fa $$\chi_{8085}(422, \cdot)$$ n/a 15104 16
8085.2.fb $$\chi_{8085}(68, \cdot)$$ n/a 15104 16
8085.2.fd $$\chi_{8085}(313, \cdot)$$ n/a 7680 16
8085.2.fg $$\chi_{8085}(508, \cdot)$$ n/a 7680 16
8085.2.fh $$\chi_{8085}(64, \cdot)$$ n/a 16128 24
8085.2.fk $$\chi_{8085}(251, \cdot)$$ n/a 21504 24
8085.2.fm $$\chi_{8085}(29, \cdot)$$ n/a 32064 24
8085.2.fn $$\chi_{8085}(601, \cdot)$$ n/a 10752 24
8085.2.fp $$\chi_{8085}(139, \cdot)$$ n/a 16128 24
8085.2.fs $$\chi_{8085}(281, \cdot)$$ n/a 21504 24
8085.2.fu $$\chi_{8085}(104, \cdot)$$ n/a 32064 24
8085.2.fx $$\chi_{8085}(397, \cdot)$$ n/a 13440 24
8085.2.fy $$\chi_{8085}(142, \cdot)$$ n/a 16128 24
8085.2.ga $$\chi_{8085}(23, \cdot)$$ n/a 26880 24
8085.2.gd $$\chi_{8085}(593, \cdot)$$ n/a 32064 24
8085.2.ge $$\chi_{8085}(16, \cdot)$$ n/a 21504 48
8085.2.gg $$\chi_{8085}(202, \cdot)$$ n/a 32256 48
8085.2.gh $$\chi_{8085}(127, \cdot)$$ n/a 32256 48
8085.2.gj $$\chi_{8085}(92, \cdot)$$ n/a 64128 48
8085.2.gm $$\chi_{8085}(62, \cdot)$$ n/a 64128 48
8085.2.gn $$\chi_{8085}(326, \cdot)$$ n/a 43008 48
8085.2.gq $$\chi_{8085}(94, \cdot)$$ n/a 32256 48
8085.2.gs $$\chi_{8085}(59, \cdot)$$ n/a 64128 48
8085.2.gu $$\chi_{8085}(26, \cdot)$$ n/a 43008 48
8085.2.gx $$\chi_{8085}(4, \cdot)$$ n/a 32256 48
8085.2.gz $$\chi_{8085}(61, \cdot)$$ n/a 21504 48
8085.2.ha $$\chi_{8085}(74, \cdot)$$ n/a 64128 48
8085.2.hc $$\chi_{8085}(17, \cdot)$$ n/a 128256 96
8085.2.hf $$\chi_{8085}(53, \cdot)$$ n/a 128256 96
8085.2.hh $$\chi_{8085}(172, \cdot)$$ n/a 64512 96
8085.2.hi $$\chi_{8085}(82, \cdot)$$ n/a 64512 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8085))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8085)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(33))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(77))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(105))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(147))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(165))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(231))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(385))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(539))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(735))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1155))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1617))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2695))$$$$^{\oplus 2}$$