# Properties

 Label 5096.2 Level 5096 Weight 2 Dimension 419361 Nonzero newspaces 90 Sturm bound 3161088

## Defining parameters

 Level: $$N$$ = $$5096 = 2^{3} \cdot 7^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$90$$ Sturm bound: $$3161088$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(5096))$$.

Total New Old
Modular forms 798912 423629 375283
Cusp forms 781633 419361 362272
Eisenstein series 17279 4268 13011

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(5096))$$

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
5096.2.a $$\chi_{5096}(1, \cdot)$$ 5096.2.a.a 1 1
5096.2.a.b 1
5096.2.a.c 1
5096.2.a.d 1
5096.2.a.e 1
5096.2.a.f 1
5096.2.a.g 1
5096.2.a.h 1
5096.2.a.i 1
5096.2.a.j 1
5096.2.a.k 1
5096.2.a.l 2
5096.2.a.m 2
5096.2.a.n 2
5096.2.a.o 2
5096.2.a.p 2
5096.2.a.q 2
5096.2.a.r 4
5096.2.a.s 4
5096.2.a.t 4
5096.2.a.u 4
5096.2.a.v 4
5096.2.a.w 4
5096.2.a.x 5
5096.2.a.y 5
5096.2.a.z 7
5096.2.a.ba 7
5096.2.a.bb 8
5096.2.a.bc 8
5096.2.a.bd 8
5096.2.a.be 8
5096.2.a.bf 10
5096.2.a.bg 10
5096.2.b $$\chi_{5096}(2547, \cdot)$$ n/a 552 1
5096.2.c $$\chi_{5096}(2549, \cdot)$$ n/a 492 1
5096.2.h $$\chi_{5096}(2939, \cdot)$$ n/a 480 1
5096.2.i $$\chi_{5096}(2157, \cdot)$$ n/a 564 1
5096.2.j $$\chi_{5096}(391, \cdot)$$ None 0 1
5096.2.k $$\chi_{5096}(4705, \cdot)$$ n/a 144 1
5096.2.p $$\chi_{5096}(5095, \cdot)$$ None 0 1
5096.2.q $$\chi_{5096}(1745, \cdot)$$ n/a 280 2
5096.2.r $$\chi_{5096}(1145, \cdot)$$ n/a 240 2
5096.2.s $$\chi_{5096}(393, \cdot)$$ n/a 286 2
5096.2.t $$\chi_{5096}(1537, \cdot)$$ n/a 280 2
5096.2.v $$\chi_{5096}(2647, \cdot)$$ None 0 2
5096.2.w $$\chi_{5096}(489, \cdot)$$ n/a 280 2
5096.2.z $$\chi_{5096}(99, \cdot)$$ n/a 1128 2
5096.2.ba $$\chi_{5096}(3037, \cdot)$$ n/a 1104 2
5096.2.be $$\chi_{5096}(1941, \cdot)$$ n/a 1104 2
5096.2.bf $$\chi_{5096}(2187, \cdot)$$ n/a 1104 2
5096.2.bg $$\chi_{5096}(373, \cdot)$$ n/a 1104 2
5096.2.bh $$\chi_{5096}(1011, \cdot)$$ n/a 1104 2
5096.2.bm $$\chi_{5096}(3137, \cdot)$$ n/a 288 2
5096.2.bn $$\chi_{5096}(783, \cdot)$$ None 0 2
5096.2.bo $$\chi_{5096}(2383, \cdot)$$ None 0 2
5096.2.bp $$\chi_{5096}(3743, \cdot)$$ None 0 2
5096.2.by $$\chi_{5096}(753, \cdot)$$ n/a 280 2
5096.2.bz $$\chi_{5096}(4135, \cdot)$$ None 0 2
5096.2.ca $$\chi_{5096}(815, \cdot)$$ None 0 2
5096.2.cb $$\chi_{5096}(569, \cdot)$$ n/a 280 2
5096.2.cc $$\chi_{5096}(3527, \cdot)$$ None 0 2
5096.2.ch $$\chi_{5096}(2941, \cdot)$$ n/a 1128 2
5096.2.ci $$\chi_{5096}(979, \cdot)$$ n/a 1104 2
5096.2.cj $$\chi_{5096}(3301, \cdot)$$ n/a 1104 2
5096.2.ck $$\chi_{5096}(1587, \cdot)$$ n/a 960 2
5096.2.cl $$\chi_{5096}(1979, \cdot)$$ n/a 1104 2
5096.2.cm $$\chi_{5096}(1733, \cdot)$$ n/a 1104 2
5096.2.cv $$\chi_{5096}(803, \cdot)$$ n/a 1104 2
5096.2.cw $$\chi_{5096}(165, \cdot)$$ n/a 1104 2
5096.2.cx $$\chi_{5096}(3693, \cdot)$$ n/a 960 2
5096.2.cy $$\chi_{5096}(1195, \cdot)$$ n/a 1104 2
5096.2.cz $$\chi_{5096}(589, \cdot)$$ n/a 1128 2
5096.2.da $$\chi_{5096}(3331, \cdot)$$ n/a 1104 2
5096.2.df $$\chi_{5096}(2175, \cdot)$$ None 0 2
5096.2.dg $$\chi_{5096}(361, \cdot)$$ n/a 280 2
5096.2.dh $$\chi_{5096}(607, \cdot)$$ None 0 2
5096.2.dk $$\chi_{5096}(729, \cdot)$$ n/a 1008 6
5096.2.dm $$\chi_{5096}(1489, \cdot)$$ n/a 560 4
5096.2.dn $$\chi_{5096}(1255, \cdot)$$ None 0 4
5096.2.dq $$\chi_{5096}(275, \cdot)$$ n/a 2208 4
5096.2.dt $$\chi_{5096}(293, \cdot)$$ n/a 2208 4
5096.2.du $$\chi_{5096}(1685, \cdot)$$ n/a 2208 4
5096.2.dv $$\chi_{5096}(2451, \cdot)$$ n/a 2256 4
5096.2.dw $$\chi_{5096}(1243, \cdot)$$ n/a 2208 4
5096.2.dz $$\chi_{5096}(509, \cdot)$$ n/a 2208 4
5096.2.ec $$\chi_{5096}(1047, \cdot)$$ None 0 4
5096.2.ef $$\chi_{5096}(97, \cdot)$$ n/a 560 4
5096.2.eg $$\chi_{5096}(1097, \cdot)$$ n/a 560 4
5096.2.eh $$\chi_{5096}(687, \cdot)$$ None 0 4
5096.2.ei $$\chi_{5096}(655, \cdot)$$ None 0 4
5096.2.el $$\chi_{5096}(1697, \cdot)$$ n/a 560 4
5096.2.eo $$\chi_{5096}(717, \cdot)$$ n/a 2208 4
5096.2.ep $$\chi_{5096}(67, \cdot)$$ n/a 2208 4
5096.2.er $$\chi_{5096}(727, \cdot)$$ None 0 6
5096.2.ew $$\chi_{5096}(337, \cdot)$$ n/a 1176 6
5096.2.ex $$\chi_{5096}(1119, \cdot)$$ None 0 6
5096.2.ey $$\chi_{5096}(701, \cdot)$$ n/a 4680 6
5096.2.ez $$\chi_{5096}(27, \cdot)$$ n/a 4032 6
5096.2.fe $$\chi_{5096}(365, \cdot)$$ n/a 4032 6
5096.2.ff $$\chi_{5096}(363, \cdot)$$ n/a 4680 6
5096.2.fg $$\chi_{5096}(9, \cdot)$$ n/a 2352 12
5096.2.fh $$\chi_{5096}(113, \cdot)$$ n/a 2352 12
5096.2.fi $$\chi_{5096}(417, \cdot)$$ n/a 2016 12
5096.2.fj $$\chi_{5096}(289, \cdot)$$ n/a 2352 12
5096.2.fl $$\chi_{5096}(125, \cdot)$$ n/a 9360 12
5096.2.fm $$\chi_{5096}(603, \cdot)$$ n/a 9360 12
5096.2.fp $$\chi_{5096}(265, \cdot)$$ n/a 2352 12
5096.2.fq $$\chi_{5096}(239, \cdot)$$ None 0 12
5096.2.fu $$\chi_{5096}(367, \cdot)$$ None 0 12
5096.2.fv $$\chi_{5096}(121, \cdot)$$ n/a 2352 12
5096.2.fw $$\chi_{5096}(647, \cdot)$$ None 0 12
5096.2.gb $$\chi_{5096}(139, \cdot)$$ n/a 9360 12
5096.2.gc $$\chi_{5096}(309, \cdot)$$ n/a 9360 12
5096.2.gd $$\chi_{5096}(467, \cdot)$$ n/a 9360 12
5096.2.ge $$\chi_{5096}(53, \cdot)$$ n/a 8064 12
5096.2.gf $$\chi_{5096}(653, \cdot)$$ n/a 9360 12
5096.2.gg $$\chi_{5096}(75, \cdot)$$ n/a 9360 12
5096.2.gp $$\chi_{5096}(205, \cdot)$$ n/a 9360 12
5096.2.gq $$\chi_{5096}(451, \cdot)$$ n/a 9360 12
5096.2.gr $$\chi_{5096}(131, \cdot)$$ n/a 8064 12
5096.2.gs $$\chi_{5096}(389, \cdot)$$ n/a 9360 12
5096.2.gt $$\chi_{5096}(251, \cdot)$$ n/a 9360 12
5096.2.gu $$\chi_{5096}(29, \cdot)$$ n/a 9360 12
5096.2.gz $$\chi_{5096}(335, \cdot)$$ None 0 12
5096.2.ha $$\chi_{5096}(641, \cdot)$$ n/a 2352 12
5096.2.hb $$\chi_{5096}(87, \cdot)$$ None 0 12
5096.2.hc $$\chi_{5096}(495, \cdot)$$ None 0 12
5096.2.hd $$\chi_{5096}(25, \cdot)$$ n/a 2352 12
5096.2.hm $$\chi_{5096}(103, \cdot)$$ None 0 12
5096.2.hn $$\chi_{5096}(199, \cdot)$$ None 0 12
5096.2.ho $$\chi_{5096}(55, \cdot)$$ None 0 12
5096.2.hp $$\chi_{5096}(225, \cdot)$$ n/a 2352 12
5096.2.hu $$\chi_{5096}(283, \cdot)$$ n/a 9360 12
5096.2.hv $$\chi_{5096}(445, \cdot)$$ n/a 9360 12
5096.2.hw $$\chi_{5096}(3, \cdot)$$ n/a 9360 12
5096.2.hx $$\chi_{5096}(485, \cdot)$$ n/a 9360 12
5096.2.ib $$\chi_{5096}(11, \cdot)$$ n/a 18720 24
5096.2.ic $$\chi_{5096}(397, \cdot)$$ n/a 18720 24
5096.2.if $$\chi_{5096}(89, \cdot)$$ n/a 4704 24
5096.2.ii $$\chi_{5096}(135, \cdot)$$ None 0 24
5096.2.ij $$\chi_{5096}(15, \cdot)$$ None 0 24
5096.2.ik $$\chi_{5096}(73, \cdot)$$ n/a 4704 24
5096.2.il $$\chi_{5096}(41, \cdot)$$ n/a 4704 24
5096.2.io $$\chi_{5096}(319, \cdot)$$ None 0 24
5096.2.ir $$\chi_{5096}(45, \cdot)$$ n/a 18720 24
5096.2.iu $$\chi_{5096}(291, \cdot)$$ n/a 18720 24
5096.2.iv $$\chi_{5096}(267, \cdot)$$ n/a 18720 24
5096.2.iw $$\chi_{5096}(5, \cdot)$$ n/a 18720 24
5096.2.ix $$\chi_{5096}(349, \cdot)$$ n/a 18720 24
5096.2.ja $$\chi_{5096}(123, \cdot)$$ n/a 18720 24
5096.2.jd $$\chi_{5096}(375, \cdot)$$ None 0 24
5096.2.je $$\chi_{5096}(33, \cdot)$$ n/a 4704 24

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(5096))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(5096)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(182))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(364))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(637))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(728))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1274))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2548))$$$$^{\oplus 2}$$