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Properties

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

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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 available 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

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