# Properties

 Label 7800.2 Level 7800 Weight 2 Dimension 617832 Nonzero newspaces 120 Sturm bound 6451200

## Defining parameters

 Level: $$N$$ = $$7800 = 2^{3} \cdot 3 \cdot 5^{2} \cdot 13$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$120$$ Sturm bound: $$6451200$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(7800))$$.

Total New Old
Modular forms 1628928 621440 1007488
Cusp forms 1596673 617832 978841
Eisenstein series 32255 3608 28647

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(7800))$$

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
7800.2.a $$\chi_{7800}(1, \cdot)$$ 7800.2.a.a 1 1
7800.2.a.b 1
7800.2.a.c 1
7800.2.a.d 1
7800.2.a.e 1
7800.2.a.f 1
7800.2.a.g 1
7800.2.a.h 1
7800.2.a.i 1
7800.2.a.j 1
7800.2.a.k 1
7800.2.a.l 1
7800.2.a.m 1
7800.2.a.n 1
7800.2.a.o 1
7800.2.a.p 1
7800.2.a.q 1
7800.2.a.r 1
7800.2.a.s 1
7800.2.a.t 1
7800.2.a.u 1
7800.2.a.v 1
7800.2.a.w 1
7800.2.a.x 1
7800.2.a.y 2
7800.2.a.z 2
7800.2.a.ba 2
7800.2.a.bb 2
7800.2.a.bc 2
7800.2.a.bd 2
7800.2.a.be 2
7800.2.a.bf 3
7800.2.a.bg 3
7800.2.a.bh 3
7800.2.a.bi 3
7800.2.a.bj 3
7800.2.a.bk 3
7800.2.a.bl 3
7800.2.a.bm 3
7800.2.a.bn 3
7800.2.a.bo 3
7800.2.a.bp 3
7800.2.a.bq 3
7800.2.a.br 3
7800.2.a.bs 3
7800.2.a.bt 4
7800.2.a.bu 4
7800.2.a.bv 4
7800.2.a.bw 4
7800.2.a.bx 4
7800.2.a.by 4
7800.2.a.bz 5
7800.2.a.ca 5
7800.2.b $$\chi_{7800}(5149, \cdot)$$ n/a 432 1
7800.2.e $$\chi_{7800}(3251, \cdot)$$ n/a 912 1
7800.2.g $$\chi_{7800}(7201, \cdot)$$ n/a 134 1
7800.2.h $$\chi_{7800}(7799, \cdot)$$ None 0 1
7800.2.k $$\chi_{7800}(7151, \cdot)$$ None 0 1
7800.2.l $$\chi_{7800}(1249, \cdot)$$ n/a 108 1
7800.2.n $$\chi_{7800}(3899, \cdot)$$ n/a 1000 1
7800.2.q $$\chi_{7800}(3301, \cdot)$$ n/a 532 1
7800.2.r $$\chi_{7800}(649, \cdot)$$ n/a 124 1
7800.2.u $$\chi_{7800}(6551, \cdot)$$ None 0 1
7800.2.w $$\chi_{7800}(3901, \cdot)$$ n/a 456 1
7800.2.x $$\chi_{7800}(4499, \cdot)$$ n/a 864 1
7800.2.ba $$\chi_{7800}(2651, \cdot)$$ n/a 1052 1
7800.2.bb $$\chi_{7800}(4549, \cdot)$$ n/a 504 1
7800.2.bd $$\chi_{7800}(599, \cdot)$$ None 0 1
7800.2.bg $$\chi_{7800}(601, \cdot)$$ n/a 264 2
7800.2.bh $$\chi_{7800}(3193, \cdot)$$ n/a 252 2
7800.2.bi $$\chi_{7800}(1643, \cdot)$$ n/a 2000 2
7800.2.bn $$\chi_{7800}(1357, \cdot)$$ n/a 1008 2
7800.2.bo $$\chi_{7800}(1607, \cdot)$$ None 0 2
7800.2.bq $$\chi_{7800}(4757, \cdot)$$ n/a 2000 2
7800.2.br $$\chi_{7800}(1457, \cdot)$$ n/a 432 2
7800.2.bu $$\chi_{7800}(6007, \cdot)$$ None 0 2
7800.2.bv $$\chi_{7800}(1507, \cdot)$$ n/a 1008 2
7800.2.by $$\chi_{7800}(4649, \cdot)$$ n/a 504 2
7800.2.bz $$\chi_{7800}(749, \cdot)$$ n/a 2000 2
7800.2.cb $$\chi_{7800}(4051, \cdot)$$ n/a 1064 2
7800.2.ce $$\chi_{7800}(151, \cdot)$$ None 0 2
7800.2.cg $$\chi_{7800}(499, \cdot)$$ n/a 1008 2
7800.2.ch $$\chi_{7800}(1399, \cdot)$$ None 0 2
7800.2.cj $$\chi_{7800}(3401, \cdot)$$ n/a 532 2
7800.2.cm $$\chi_{7800}(2501, \cdot)$$ n/a 2104 2
7800.2.cn $$\chi_{7800}(5407, \cdot)$$ None 0 2
7800.2.cq $$\chi_{7800}(2107, \cdot)$$ n/a 864 2
7800.2.cr $$\chi_{7800}(5357, \cdot)$$ n/a 1728 2
7800.2.cu $$\chi_{7800}(857, \cdot)$$ n/a 504 2
7800.2.cx $$\chi_{7800}(707, \cdot)$$ n/a 2000 2
7800.2.cy $$\chi_{7800}(2257, \cdot)$$ n/a 252 2
7800.2.cz $$\chi_{7800}(2543, \cdot)$$ None 0 2
7800.2.da $$\chi_{7800}(2293, \cdot)$$ n/a 1008 2
7800.2.dd $$\chi_{7800}(1561, \cdot)$$ n/a 720 4
7800.2.dg $$\chi_{7800}(1199, \cdot)$$ None 0 2
7800.2.di $$\chi_{7800}(2149, \cdot)$$ n/a 1008 2
7800.2.dj $$\chi_{7800}(251, \cdot)$$ n/a 2104 2
7800.2.dm $$\chi_{7800}(5099, \cdot)$$ n/a 2000 2
7800.2.dn $$\chi_{7800}(4501, \cdot)$$ n/a 1064 2
7800.2.dp $$\chi_{7800}(4151, \cdot)$$ None 0 2
7800.2.ds $$\chi_{7800}(49, \cdot)$$ n/a 248 2
7800.2.dt $$\chi_{7800}(901, \cdot)$$ n/a 1064 2
7800.2.dw $$\chi_{7800}(1499, \cdot)$$ n/a 2000 2
7800.2.dy $$\chi_{7800}(1849, \cdot)$$ n/a 256 2
7800.2.dz $$\chi_{7800}(1751, \cdot)$$ None 0 2
7800.2.ec $$\chi_{7800}(5399, \cdot)$$ None 0 2
7800.2.ed $$\chi_{7800}(4801, \cdot)$$ n/a 268 2
7800.2.ef $$\chi_{7800}(3851, \cdot)$$ n/a 2104 2
7800.2.ei $$\chi_{7800}(5749, \cdot)$$ n/a 1008 2
7800.2.ej $$\chi_{7800}(181, \cdot)$$ n/a 3360 4
7800.2.em $$\chi_{7800}(779, \cdot)$$ n/a 6688 4
7800.2.eo $$\chi_{7800}(2809, \cdot)$$ n/a 720 4
7800.2.ep $$\chi_{7800}(911, \cdot)$$ None 0 4
7800.2.es $$\chi_{7800}(1559, \cdot)$$ None 0 4
7800.2.et $$\chi_{7800}(961, \cdot)$$ n/a 832 4
7800.2.ev $$\chi_{7800}(131, \cdot)$$ n/a 5760 4
7800.2.ey $$\chi_{7800}(469, \cdot)$$ n/a 2880 4
7800.2.fb $$\chi_{7800}(2159, \cdot)$$ None 0 4
7800.2.fd $$\chi_{7800}(1429, \cdot)$$ n/a 3360 4
7800.2.fe $$\chi_{7800}(1091, \cdot)$$ n/a 6688 4
7800.2.fh $$\chi_{7800}(1379, \cdot)$$ n/a 5760 4
7800.2.fi $$\chi_{7800}(781, \cdot)$$ n/a 2880 4
7800.2.fk $$\chi_{7800}(311, \cdot)$$ None 0 4
7800.2.fn $$\chi_{7800}(2209, \cdot)$$ n/a 848 4
7800.2.fq $$\chi_{7800}(1007, \cdot)$$ None 0 4
7800.2.fr $$\chi_{7800}(1957, \cdot)$$ n/a 2016 4
7800.2.fs $$\chi_{7800}(2243, \cdot)$$ n/a 4000 4
7800.2.ft $$\chi_{7800}(1393, \cdot)$$ n/a 504 4
7800.2.fw $$\chi_{7800}(257, \cdot)$$ n/a 1008 4
7800.2.fz $$\chi_{7800}(893, \cdot)$$ n/a 4000 4
7800.2.ga $$\chi_{7800}(2707, \cdot)$$ n/a 2016 4
7800.2.gd $$\chi_{7800}(3007, \cdot)$$ None 0 4
7800.2.gf $$\chi_{7800}(3101, \cdot)$$ n/a 4208 4
7800.2.gg $$\chi_{7800}(401, \cdot)$$ n/a 1064 4
7800.2.gi $$\chi_{7800}(799, \cdot)$$ None 0 4
7800.2.gl $$\chi_{7800}(1099, \cdot)$$ n/a 2016 4
7800.2.gn $$\chi_{7800}(3751, \cdot)$$ None 0 4
7800.2.go $$\chi_{7800}(1051, \cdot)$$ n/a 2128 4
7800.2.gq $$\chi_{7800}(149, \cdot)$$ n/a 4000 4
7800.2.gt $$\chi_{7800}(449, \cdot)$$ n/a 1008 4
7800.2.gv $$\chi_{7800}(43, \cdot)$$ n/a 2016 4
7800.2.gw $$\chi_{7800}(607, \cdot)$$ None 0 4
7800.2.gz $$\chi_{7800}(2057, \cdot)$$ n/a 1008 4
7800.2.ha $$\chi_{7800}(2357, \cdot)$$ n/a 4000 4
7800.2.hc $$\chi_{7800}(2893, \cdot)$$ n/a 2016 4
7800.2.hd $$\chi_{7800}(743, \cdot)$$ None 0 4
7800.2.hi $$\chi_{7800}(193, \cdot)$$ n/a 504 4
7800.2.hj $$\chi_{7800}(1307, \cdot)$$ n/a 4000 4
7800.2.hk $$\chi_{7800}(841, \cdot)$$ n/a 1696 8
7800.2.hl $$\chi_{7800}(47, \cdot)$$ None 0 8
7800.2.hm $$\chi_{7800}(853, \cdot)$$ n/a 6720 8
7800.2.hr $$\chi_{7800}(83, \cdot)$$ n/a 13376 8
7800.2.hs $$\chi_{7800}(73, \cdot)$$ n/a 1680 8
7800.2.ht $$\chi_{7800}(233, \cdot)$$ n/a 3360 8
7800.2.hw $$\chi_{7800}(53, \cdot)$$ n/a 11520 8
7800.2.hx $$\chi_{7800}(547, \cdot)$$ n/a 5760 8
7800.2.ia $$\chi_{7800}(103, \cdot)$$ None 0 8
7800.2.ib $$\chi_{7800}(941, \cdot)$$ n/a 13376 8
7800.2.ie $$\chi_{7800}(161, \cdot)$$ n/a 3360 8
7800.2.ig $$\chi_{7800}(1279, \cdot)$$ None 0 8
7800.2.ih $$\chi_{7800}(619, \cdot)$$ n/a 6720 8
7800.2.ij $$\chi_{7800}(31, \cdot)$$ None 0 8
7800.2.im $$\chi_{7800}(811, \cdot)$$ n/a 6720 8
7800.2.io $$\chi_{7800}(629, \cdot)$$ n/a 13376 8
7800.2.ip $$\chi_{7800}(1409, \cdot)$$ n/a 3360 8
7800.2.is $$\chi_{7800}(883, \cdot)$$ n/a 6720 8
7800.2.it $$\chi_{7800}(703, \cdot)$$ None 0 8
7800.2.iw $$\chi_{7800}(833, \cdot)$$ n/a 2880 8
7800.2.ix $$\chi_{7800}(77, \cdot)$$ n/a 13376 8
7800.2.jb $$\chi_{7800}(733, \cdot)$$ n/a 6720 8
7800.2.jc $$\chi_{7800}(983, \cdot)$$ None 0 8
7800.2.jd $$\chi_{7800}(697, \cdot)$$ n/a 1680 8
7800.2.je $$\chi_{7800}(203, \cdot)$$ n/a 13376 8
7800.2.jh $$\chi_{7800}(1369, \cdot)$$ n/a 1696 8
7800.2.jk $$\chi_{7800}(1031, \cdot)$$ None 0 8
7800.2.jm $$\chi_{7800}(61, \cdot)$$ n/a 6720 8
7800.2.jn $$\chi_{7800}(419, \cdot)$$ n/a 13376 8
7800.2.jq $$\chi_{7800}(491, \cdot)$$ n/a 13376 8
7800.2.jr $$\chi_{7800}(589, \cdot)$$ n/a 6720 8
7800.2.jt $$\chi_{7800}(1439, \cdot)$$ None 0 8
7800.2.jw $$\chi_{7800}(1069, \cdot)$$ n/a 6720 8
7800.2.jz $$\chi_{7800}(731, \cdot)$$ n/a 13376 8
7800.2.kb $$\chi_{7800}(121, \cdot)$$ n/a 1664 8
7800.2.kc $$\chi_{7800}(719, \cdot)$$ None 0 8
7800.2.kf $$\chi_{7800}(191, \cdot)$$ None 0 8
7800.2.kg $$\chi_{7800}(289, \cdot)$$ n/a 1664 8
7800.2.ki $$\chi_{7800}(179, \cdot)$$ n/a 13376 8
7800.2.kl $$\chi_{7800}(1141, \cdot)$$ n/a 6720 8
7800.2.ko $$\chi_{7800}(817, \cdot)$$ n/a 3360 16
7800.2.kp $$\chi_{7800}(227, \cdot)$$ n/a 26752 16
7800.2.kq $$\chi_{7800}(37, \cdot)$$ n/a 13440 16
7800.2.kr $$\chi_{7800}(1103, \cdot)$$ None 0 16
7800.2.kv $$\chi_{7800}(173, \cdot)$$ n/a 26752 16
7800.2.kw $$\chi_{7800}(113, \cdot)$$ n/a 6720 16
7800.2.kz $$\chi_{7800}(367, \cdot)$$ None 0 16
7800.2.la $$\chi_{7800}(283, \cdot)$$ n/a 13440 16
7800.2.lc $$\chi_{7800}(89, \cdot)$$ n/a 6720 16
7800.2.lf $$\chi_{7800}(509, \cdot)$$ n/a 26752 16
7800.2.lh $$\chi_{7800}(331, \cdot)$$ n/a 13440 16
7800.2.li $$\chi_{7800}(271, \cdot)$$ None 0 16
7800.2.lk $$\chi_{7800}(19, \cdot)$$ n/a 13440 16
7800.2.ln $$\chi_{7800}(319, \cdot)$$ None 0 16
7800.2.lp $$\chi_{7800}(41, \cdot)$$ n/a 6720 16
7800.2.lq $$\chi_{7800}(461, \cdot)$$ n/a 26752 16
7800.2.ls $$\chi_{7800}(127, \cdot)$$ None 0 16
7800.2.lv $$\chi_{7800}(523, \cdot)$$ n/a 13440 16
7800.2.lw $$\chi_{7800}(653, \cdot)$$ n/a 26752 16
7800.2.lz $$\chi_{7800}(17, \cdot)$$ n/a 6720 16
7800.2.ma $$\chi_{7800}(947, \cdot)$$ n/a 26752 16
7800.2.mb $$\chi_{7800}(97, \cdot)$$ n/a 3360 16
7800.2.mg $$\chi_{7800}(167, \cdot)$$ None 0 16
7800.2.mh $$\chi_{7800}(877, \cdot)$$ n/a 13440 16

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(7800))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(7800)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 24}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(15))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(20))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(24))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(25))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(26))$$$$^{\oplus 18}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(30))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(40))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(50))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(52))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(60))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(65))$$$$^{\oplus 16}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(75))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(78))$$$$^{\oplus 9}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(100))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(104))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(120))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(130))$$$$^{\oplus 12}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(150))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(156))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(195))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(200))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(260))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(300))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(312))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(325))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(390))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(520))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(600))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(650))$$$$^{\oplus 6}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(780))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(975))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1300))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1560))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1950))$$$$^{\oplus 3}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2600))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(3900))$$$$^{\oplus 2}$$