# Properties

 Label 9680.2 Level 9680 Weight 2 Dimension 1410026 Nonzero newspaces 56 Sturm bound 11151360

## Defining parameters

 Level: $$N$$ = $$9680 = 2^{4} \cdot 5 \cdot 11^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$56$$ Sturm bound: $$11151360$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9680))$$.

Total New Old
Modular forms 2805760 1417612 1388148
Cusp forms 2769921 1410026 1359895
Eisenstein series 35839 7586 28253

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9680))$$

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
9680.2.a $$\chi_{9680}(1, \cdot)$$ 9680.2.a.a 1 1
9680.2.a.b 1
9680.2.a.c 1
9680.2.a.d 1
9680.2.a.e 1
9680.2.a.f 1
9680.2.a.g 1
9680.2.a.h 1
9680.2.a.i 1
9680.2.a.j 1
9680.2.a.k 1
9680.2.a.l 1
9680.2.a.m 1
9680.2.a.n 1
9680.2.a.o 1
9680.2.a.p 1
9680.2.a.q 1
9680.2.a.r 1
9680.2.a.s 1
9680.2.a.t 1
9680.2.a.u 1
9680.2.a.v 1
9680.2.a.w 1
9680.2.a.x 1
9680.2.a.y 1
9680.2.a.z 1
9680.2.a.ba 1
9680.2.a.bb 1
9680.2.a.bc 1
9680.2.a.bd 1
9680.2.a.be 1
9680.2.a.bf 1
9680.2.a.bg 2
9680.2.a.bh 2
9680.2.a.bi 2
9680.2.a.bj 2
9680.2.a.bk 2
9680.2.a.bl 2
9680.2.a.bm 2
9680.2.a.bn 2
9680.2.a.bo 2
9680.2.a.bp 2
9680.2.a.bq 2
9680.2.a.br 2
9680.2.a.bs 2
9680.2.a.bt 2
9680.2.a.bu 2
9680.2.a.bv 2
9680.2.a.bw 2
9680.2.a.bx 2
9680.2.a.by 3
9680.2.a.bz 3
9680.2.a.ca 3
9680.2.a.cb 3
9680.2.a.cc 3
9680.2.a.cd 3
9680.2.a.ce 3
9680.2.a.cf 3
9680.2.a.cg 3
9680.2.a.ch 3
9680.2.a.ci 4
9680.2.a.cj 4
9680.2.a.ck 4
9680.2.a.cl 4
9680.2.a.cm 4
9680.2.a.cn 4
9680.2.a.co 4
9680.2.a.cp 4
9680.2.a.cq 4
9680.2.a.cr 4
9680.2.a.cs 4
9680.2.a.ct 4
9680.2.a.cu 4
9680.2.a.cv 4
9680.2.a.cw 6
9680.2.a.cx 6
9680.2.a.cy 6
9680.2.a.cz 6
9680.2.a.da 6
9680.2.a.db 6
9680.2.a.dc 6
9680.2.a.dd 6
9680.2.a.de 8
9680.2.a.df 8
9680.2.b $$\chi_{9680}(5809, \cdot)$$ n/a 318 1
9680.2.c $$\chi_{9680}(4839, \cdot)$$ None 0 1
9680.2.f $$\chi_{9680}(3871, \cdot)$$ n/a 216 1
9680.2.g $$\chi_{9680}(4841, \cdot)$$ None 0 1
9680.2.l $$\chi_{9680}(969, \cdot)$$ None 0 1
9680.2.m $$\chi_{9680}(9679, \cdot)$$ n/a 324 1
9680.2.p $$\chi_{9680}(8711, \cdot)$$ None 0 1
9680.2.s $$\chi_{9680}(5083, \cdot)$$ n/a 2580 2
9680.2.t $$\chi_{9680}(1693, \cdot)$$ n/a 2560 2
9680.2.v $$\chi_{9680}(1451, \cdot)$$ n/a 1728 2
9680.2.w $$\chi_{9680}(2421, \cdot)$$ n/a 1744 2
9680.2.z $$\chi_{9680}(727, \cdot)$$ None 0 2
9680.2.bb $$\chi_{9680}(7017, \cdot)$$ None 0 2
9680.2.bd $$\chi_{9680}(2177, \cdot)$$ n/a 632 2
9680.2.bf $$\chi_{9680}(5567, \cdot)$$ n/a 654 2
9680.2.bh $$\chi_{9680}(3389, \cdot)$$ n/a 2580 2
9680.2.bi $$\chi_{9680}(2419, \cdot)$$ n/a 2560 2
9680.2.bk $$\chi_{9680}(243, \cdot)$$ n/a 2580 2
9680.2.bl $$\chi_{9680}(6533, \cdot)$$ n/a 2560 2
9680.2.bo $$\chi_{9680}(81, \cdot)$$ n/a 864 4
9680.2.bp $$\chi_{9680}(2151, \cdot)$$ None 0 4
9680.2.bs $$\chi_{9680}(239, \cdot)$$ n/a 1296 4
9680.2.bt $$\chi_{9680}(9, \cdot)$$ None 0 4
9680.2.by $$\chi_{9680}(1721, \cdot)$$ None 0 4
9680.2.bz $$\chi_{9680}(3791, \cdot)$$ n/a 864 4
9680.2.cc $$\chi_{9680}(4759, \cdot)$$ None 0 4
9680.2.cd $$\chi_{9680}(2689, \cdot)$$ n/a 1264 4
9680.2.ce $$\chi_{9680}(881, \cdot)$$ n/a 2640 10
9680.2.ch $$\chi_{9680}(717, \cdot)$$ n/a 10240 8
9680.2.ci $$\chi_{9680}(3, \cdot)$$ n/a 10240 8
9680.2.cj $$\chi_{9680}(699, \cdot)$$ n/a 10240 8
9680.2.cm $$\chi_{9680}(269, \cdot)$$ n/a 10240 8
9680.2.cn $$\chi_{9680}(2097, \cdot)$$ n/a 2528 8
9680.2.cp $$\chi_{9680}(2447, \cdot)$$ n/a 2592 8
9680.2.cr $$\chi_{9680}(487, \cdot)$$ None 0 8
9680.2.ct $$\chi_{9680}(233, \cdot)$$ None 0 8
9680.2.cv $$\chi_{9680}(1461, \cdot)$$ n/a 6912 8
9680.2.cy $$\chi_{9680}(1371, \cdot)$$ n/a 6912 8
9680.2.cz $$\chi_{9680}(1613, \cdot)$$ n/a 10240 8
9680.2.da $$\chi_{9680}(1963, \cdot)$$ n/a 10240 8
9680.2.df $$\chi_{9680}(441, \cdot)$$ None 0 10
9680.2.dg $$\chi_{9680}(351, \cdot)$$ n/a 2640 10
9680.2.dj $$\chi_{9680}(439, \cdot)$$ None 0 10
9680.2.dk $$\chi_{9680}(529, \cdot)$$ n/a 3940 10
9680.2.dl $$\chi_{9680}(791, \cdot)$$ None 0 10
9680.2.do $$\chi_{9680}(879, \cdot)$$ n/a 3960 10
9680.2.dp $$\chi_{9680}(89, \cdot)$$ None 0 10
9680.2.ds $$\chi_{9680}(197, \cdot)$$ n/a 31600 20
9680.2.dt $$\chi_{9680}(67, \cdot)$$ n/a 31600 20
9680.2.dx $$\chi_{9680}(219, \cdot)$$ n/a 31600 20
9680.2.dy $$\chi_{9680}(309, \cdot)$$ n/a 31600 20
9680.2.ea $$\chi_{9680}(287, \cdot)$$ n/a 7920 20
9680.2.ec $$\chi_{9680}(417, \cdot)$$ n/a 7880 20
9680.2.ee $$\chi_{9680}(153, \cdot)$$ None 0 20
9680.2.eg $$\chi_{9680}(23, \cdot)$$ None 0 20
9680.2.ej $$\chi_{9680}(221, \cdot)$$ n/a 21120 20
9680.2.ek $$\chi_{9680}(131, \cdot)$$ n/a 21120 20
9680.2.eo $$\chi_{9680}(373, \cdot)$$ n/a 31600 20
9680.2.ep $$\chi_{9680}(507, \cdot)$$ n/a 31600 20
9680.2.eq $$\chi_{9680}(401, \cdot)$$ n/a 10560 40
9680.2.et $$\chi_{9680}(169, \cdot)$$ None 0 40
9680.2.eu $$\chi_{9680}(79, \cdot)$$ n/a 15840 40
9680.2.ex $$\chi_{9680}(151, \cdot)$$ None 0 40
9680.2.ey $$\chi_{9680}(49, \cdot)$$ n/a 15760 40
9680.2.ez $$\chi_{9680}(39, \cdot)$$ None 0 40
9680.2.fc $$\chi_{9680}(271, \cdot)$$ n/a 10560 40
9680.2.fd $$\chi_{9680}(201, \cdot)$$ None 0 40
9680.2.fg $$\chi_{9680}(163, \cdot)$$ n/a 126400 80
9680.2.fh $$\chi_{9680}(237, \cdot)$$ n/a 126400 80
9680.2.fk $$\chi_{9680}(51, \cdot)$$ n/a 84480 80
9680.2.fn $$\chi_{9680}(141, \cdot)$$ n/a 84480 80
9680.2.fp $$\chi_{9680}(57, \cdot)$$ None 0 80
9680.2.fr $$\chi_{9680}(103, \cdot)$$ None 0 80
9680.2.ft $$\chi_{9680}(47, \cdot)$$ n/a 31680 80
9680.2.fv $$\chi_{9680}(17, \cdot)$$ n/a 31520 80
9680.2.fw $$\chi_{9680}(69, \cdot)$$ n/a 126400 80
9680.2.fz $$\chi_{9680}(19, \cdot)$$ n/a 126400 80
9680.2.gc $$\chi_{9680}(147, \cdot)$$ n/a 126400 80
9680.2.gd $$\chi_{9680}(13, \cdot)$$ n/a 126400 80

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9680))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9680)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(1))$$$$^{\oplus 30}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(5))$$$$^{\oplus 15}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(8))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(10))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(11))$$$$^{\oplus 20}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(16))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(22))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(44))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(55))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(80))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(88))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(110))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(121))$$$$^{\oplus 10}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(176))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(220))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(242))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(440))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(484))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(605))$$$$^{\oplus 5}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(880))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(968))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1210))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1936))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2420))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4840))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(9680))$$$$^{\oplus 1}$$