# Properties

 Label 9800.2 Level 9800 Weight 2 Dimension 1400159 Nonzero newspaces 72 Sturm bound 11289600

## Defining parameters

 Level: $$N$$ = $$9800 = 2^{3} \cdot 5^{2} \cdot 7^{2}$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$72$$ Sturm bound: $$11289600$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(9800))$$.

Total New Old
Modular forms 2842560 1408113 1434447
Cusp forms 2802241 1400159 1402082
Eisenstein series 40319 7954 32365

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(9800))$$

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
9800.2.a $$\chi_{9800}(1, \cdot)$$ 9800.2.a.a 1 1
9800.2.a.b 1
9800.2.a.c 1
9800.2.a.d 1
9800.2.a.e 1
9800.2.a.f 1
9800.2.a.g 1
9800.2.a.h 1
9800.2.a.i 1
9800.2.a.j 1
9800.2.a.k 1
9800.2.a.l 1
9800.2.a.m 1
9800.2.a.n 1
9800.2.a.o 1
9800.2.a.p 1
9800.2.a.q 1
9800.2.a.r 1
9800.2.a.s 1
9800.2.a.t 1
9800.2.a.u 1
9800.2.a.v 1
9800.2.a.w 1
9800.2.a.x 1
9800.2.a.y 1
9800.2.a.z 1
9800.2.a.ba 1
9800.2.a.bb 1
9800.2.a.bc 1
9800.2.a.bd 1
9800.2.a.be 1
9800.2.a.bf 1
9800.2.a.bg 1
9800.2.a.bh 1
9800.2.a.bi 1
9800.2.a.bj 1
9800.2.a.bk 1
9800.2.a.bl 1
9800.2.a.bm 1
9800.2.a.bn 1
9800.2.a.bo 1
9800.2.a.bp 1
9800.2.a.bq 1
9800.2.a.br 2
9800.2.a.bs 2
9800.2.a.bt 2
9800.2.a.bu 2
9800.2.a.bv 2
9800.2.a.bw 2
9800.2.a.bx 2
9800.2.a.by 2
9800.2.a.bz 2
9800.2.a.ca 2
9800.2.a.cb 3
9800.2.a.cc 3
9800.2.a.cd 3
9800.2.a.ce 3
9800.2.a.cf 3
9800.2.a.cg 3
9800.2.a.ch 3
9800.2.a.ci 3
9800.2.a.cj 4
9800.2.a.ck 4
9800.2.a.cl 4
9800.2.a.cm 4
9800.2.a.cn 4
9800.2.a.co 4
9800.2.a.cp 4
9800.2.a.cq 4
9800.2.a.cr 4
9800.2.a.cs 4
9800.2.a.ct 4
9800.2.a.cu 4
9800.2.a.cv 6
9800.2.a.cw 6
9800.2.a.cx 6
9800.2.a.cy 6
9800.2.a.cz 8
9800.2.a.da 8
9800.2.a.db 10
9800.2.a.dc 10
9800.2.b $$\chi_{9800}(4901, \cdot)$$ n/a 764 1
9800.2.e $$\chi_{9800}(9799, \cdot)$$ None 0 1
9800.2.g $$\chi_{9800}(7449, \cdot)$$ n/a 184 1
9800.2.h $$\chi_{9800}(7251, \cdot)$$ n/a 748 1
9800.2.k $$\chi_{9800}(2351, \cdot)$$ None 0 1
9800.2.l $$\chi_{9800}(2549, \cdot)$$ n/a 728 1
9800.2.n $$\chi_{9800}(4899, \cdot)$$ n/a 712 1
9800.2.q $$\chi_{9800}(8201, \cdot)$$ n/a 380 2
9800.2.s $$\chi_{9800}(293, \cdot)$$ n/a 1424 2
9800.2.t $$\chi_{9800}(4607, \cdot)$$ None 0 2
9800.2.w $$\chi_{9800}(2843, \cdot)$$ n/a 1456 2
9800.2.x $$\chi_{9800}(2057, \cdot)$$ n/a 360 2
9800.2.z $$\chi_{9800}(1961, \cdot)$$ n/a 1228 4
9800.2.bb $$\chi_{9800}(5899, \cdot)$$ n/a 1424 2
9800.2.bd $$\chi_{9800}(3351, \cdot)$$ None 0 2
9800.2.bg $$\chi_{9800}(949, \cdot)$$ n/a 1424 2
9800.2.bh $$\chi_{9800}(5849, \cdot)$$ n/a 360 2
9800.2.bk $$\chi_{9800}(8251, \cdot)$$ n/a 1496 2
9800.2.bm $$\chi_{9800}(3301, \cdot)$$ n/a 1496 2
9800.2.bn $$\chi_{9800}(999, \cdot)$$ None 0 2
9800.2.bp $$\chi_{9800}(1401, \cdot)$$ n/a 1596 6
9800.2.bs $$\chi_{9800}(979, \cdot)$$ n/a 4768 4
9800.2.bu $$\chi_{9800}(589, \cdot)$$ n/a 4880 4
9800.2.bv $$\chi_{9800}(391, \cdot)$$ None 0 4
9800.2.by $$\chi_{9800}(1371, \cdot)$$ n/a 4768 4
9800.2.bz $$\chi_{9800}(1569, \cdot)$$ n/a 1232 4
9800.2.cb $$\chi_{9800}(1959, \cdot)$$ None 0 4
9800.2.ce $$\chi_{9800}(981, \cdot)$$ n/a 4880 4
9800.2.cf $$\chi_{9800}(3057, \cdot)$$ n/a 720 4
9800.2.ci $$\chi_{9800}(1243, \cdot)$$ n/a 2848 4
9800.2.cj $$\chi_{9800}(3007, \cdot)$$ None 0 4
9800.2.cm $$\chi_{9800}(1293, \cdot)$$ n/a 2848 4
9800.2.co $$\chi_{9800}(699, \cdot)$$ n/a 6024 6
9800.2.cq $$\chi_{9800}(1149, \cdot)$$ n/a 6024 6
9800.2.ct $$\chi_{9800}(951, \cdot)$$ None 0 6
9800.2.cu $$\chi_{9800}(251, \cdot)$$ n/a 6348 6
9800.2.cx $$\chi_{9800}(449, \cdot)$$ n/a 1512 6
9800.2.cz $$\chi_{9800}(1399, \cdot)$$ None 0 6
9800.2.da $$\chi_{9800}(701, \cdot)$$ n/a 6348 6
9800.2.dc $$\chi_{9800}(361, \cdot)$$ n/a 2400 8
9800.2.de $$\chi_{9800}(97, \cdot)$$ n/a 2400 8
9800.2.df $$\chi_{9800}(883, \cdot)$$ n/a 9760 8
9800.2.di $$\chi_{9800}(687, \cdot)$$ None 0 8
9800.2.dj $$\chi_{9800}(1077, \cdot)$$ n/a 9536 8
9800.2.dl $$\chi_{9800}(401, \cdot)$$ n/a 3192 12
9800.2.dm $$\chi_{9800}(43, \cdot)$$ n/a 12048 12
9800.2.dp $$\chi_{9800}(657, \cdot)$$ n/a 3024 12
9800.2.dq $$\chi_{9800}(1357, \cdot)$$ n/a 12048 12
9800.2.dt $$\chi_{9800}(407, \cdot)$$ None 0 12
9800.2.dv $$\chi_{9800}(2959, \cdot)$$ None 0 8
9800.2.dw $$\chi_{9800}(1341, \cdot)$$ n/a 9536 8
9800.2.dy $$\chi_{9800}(411, \cdot)$$ n/a 9536 8
9800.2.eb $$\chi_{9800}(569, \cdot)$$ n/a 2400 8
9800.2.ec $$\chi_{9800}(2909, \cdot)$$ n/a 9536 8
9800.2.ef $$\chi_{9800}(31, \cdot)$$ None 0 8
9800.2.eh $$\chi_{9800}(19, \cdot)$$ n/a 9536 8
9800.2.ej $$\chi_{9800}(281, \cdot)$$ n/a 10080 24
9800.2.ek $$\chi_{9800}(199, \cdot)$$ None 0 12
9800.2.en $$\chi_{9800}(501, \cdot)$$ n/a 12696 12
9800.2.ep $$\chi_{9800}(451, \cdot)$$ n/a 12696 12
9800.2.eq $$\chi_{9800}(249, \cdot)$$ n/a 3024 12
9800.2.et $$\chi_{9800}(149, \cdot)$$ n/a 12048 12
9800.2.eu $$\chi_{9800}(551, \cdot)$$ None 0 12
9800.2.ey $$\chi_{9800}(299, \cdot)$$ n/a 12048 12
9800.2.ez $$\chi_{9800}(117, \cdot)$$ n/a 19072 16
9800.2.fc $$\chi_{9800}(263, \cdot)$$ None 0 16
9800.2.fd $$\chi_{9800}(67, \cdot)$$ n/a 19072 16
9800.2.fg $$\chi_{9800}(313, \cdot)$$ n/a 4800 16
9800.2.fi $$\chi_{9800}(141, \cdot)$$ n/a 40224 24
9800.2.fj $$\chi_{9800}(279, \cdot)$$ None 0 24
9800.2.fl $$\chi_{9800}(169, \cdot)$$ n/a 10080 24
9800.2.fo $$\chi_{9800}(531, \cdot)$$ n/a 40224 24
9800.2.fp $$\chi_{9800}(111, \cdot)$$ None 0 24
9800.2.fs $$\chi_{9800}(29, \cdot)$$ n/a 40224 24
9800.2.fu $$\chi_{9800}(139, \cdot)$$ n/a 40224 24
9800.2.fx $$\chi_{9800}(207, \cdot)$$ None 0 24
9800.2.fy $$\chi_{9800}(157, \cdot)$$ n/a 24096 24
9800.2.gb $$\chi_{9800}(257, \cdot)$$ n/a 6048 24
9800.2.gc $$\chi_{9800}(107, \cdot)$$ n/a 24096 24
9800.2.ge $$\chi_{9800}(81, \cdot)$$ n/a 20160 48
9800.2.gf $$\chi_{9800}(127, \cdot)$$ None 0 48
9800.2.gi $$\chi_{9800}(13, \cdot)$$ n/a 80448 48
9800.2.gj $$\chi_{9800}(153, \cdot)$$ n/a 20160 48
9800.2.gm $$\chi_{9800}(267, \cdot)$$ n/a 80448 48
9800.2.gn $$\chi_{9800}(59, \cdot)$$ n/a 80448 48
9800.2.gr $$\chi_{9800}(271, \cdot)$$ None 0 48
9800.2.gs $$\chi_{9800}(109, \cdot)$$ n/a 80448 48
9800.2.gv $$\chi_{9800}(9, \cdot)$$ n/a 20160 48
9800.2.gw $$\chi_{9800}(131, \cdot)$$ n/a 80448 48
9800.2.gy $$\chi_{9800}(221, \cdot)$$ n/a 80448 48
9800.2.hb $$\chi_{9800}(159, \cdot)$$ None 0 48
9800.2.hd $$\chi_{9800}(123, \cdot)$$ n/a 160896 96
9800.2.he $$\chi_{9800}(17, \cdot)$$ n/a 40320 96
9800.2.hh $$\chi_{9800}(173, \cdot)$$ n/a 160896 96
9800.2.hi $$\chi_{9800}(23, \cdot)$$ None 0 96

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(9800))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(9800)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(14))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(28))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(35))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(49))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(56))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(70))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(98))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(140))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(175))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(196))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(245))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(280))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(350))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(392))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(490))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(700))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(980))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1225))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1400))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1960))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2450))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(4900))$$$$^{\oplus 2}$$