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Properties

Label 4788.2
Level 4788
Weight 2
Dimension 272254
Nonzero newspaces 184
Sturm bound 2488320

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Defining parameters

Level: \( N \) = \( 4788 = 2^{2} \cdot 3^{2} \cdot 7 \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 184 \)
Sturm bound: \(2488320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4788))\).

Total New Old
Modular forms 630720 275310 355410
Cusp forms 613441 272254 341187
Eisenstein series 17279 3056 14223

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4788))\)

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
4788.2.a \(\chi_{4788}(1, \cdot)\) 4788.2.a.a 1 1
4788.2.a.b 1
4788.2.a.c 1
4788.2.a.d 1
4788.2.a.e 1
4788.2.a.f 1
4788.2.a.g 2
4788.2.a.h 2
4788.2.a.i 2
4788.2.a.j 2
4788.2.a.k 2
4788.2.a.l 2
4788.2.a.m 2
4788.2.a.n 2
4788.2.a.o 3
4788.2.a.p 3
4788.2.a.q 4
4788.2.a.r 4
4788.2.a.s 4
4788.2.a.t 6
4788.2.b \(\chi_{4788}(1709, \cdot)\) 4788.2.b.a 2 1
4788.2.b.b 2
4788.2.b.c 16
4788.2.b.d 20
4788.2.c \(\chi_{4788}(3079, \cdot)\) n/a 360 1
4788.2.h \(\chi_{4788}(1331, \cdot)\) n/a 216 1
4788.2.i \(\chi_{4788}(3457, \cdot)\) 4788.2.i.a 2 1
4788.2.i.b 2
4788.2.i.c 4
4788.2.i.d 8
4788.2.i.e 8
4788.2.i.f 14
4788.2.i.g 14
4788.2.i.h 16
4788.2.j \(\chi_{4788}(4409, \cdot)\) 4788.2.j.a 48 1
4788.2.k \(\chi_{4788}(379, \cdot)\) n/a 300 1
4788.2.p \(\chi_{4788}(4787, \cdot)\) n/a 320 1
4788.2.q \(\chi_{4788}(3649, \cdot)\) n/a 288 2
4788.2.r \(\chi_{4788}(121, \cdot)\) n/a 320 2
4788.2.s \(\chi_{4788}(1597, \cdot)\) n/a 216 2
4788.2.t \(\chi_{4788}(2557, \cdot)\) n/a 132 2
4788.2.u \(\chi_{4788}(1369, \cdot)\) n/a 120 2
4788.2.v \(\chi_{4788}(2101, \cdot)\) n/a 240 2
4788.2.w \(\chi_{4788}(505, \cdot)\) 4788.2.w.a 2 2
4788.2.w.b 2
4788.2.w.c 2
4788.2.w.d 8
4788.2.w.e 8
4788.2.w.f 8
4788.2.w.g 8
4788.2.w.h 10
4788.2.w.i 12
4788.2.w.j 20
4788.2.w.k 20
4788.2.x \(\chi_{4788}(961, \cdot)\) n/a 320 2
4788.2.y \(\chi_{4788}(1717, \cdot)\) n/a 320 2
4788.2.z \(\chi_{4788}(1873, \cdot)\) n/a 132 2
4788.2.ba \(\chi_{4788}(2857, \cdot)\) n/a 240 2
4788.2.bb \(\chi_{4788}(1033, \cdot)\) n/a 320 2
4788.2.bc \(\chi_{4788}(457, \cdot)\) n/a 288 2
4788.2.bf \(\chi_{4788}(3307, \cdot)\) n/a 1728 2
4788.2.bg \(\chi_{4788}(569, \cdot)\) n/a 320 2
4788.2.bj \(\chi_{4788}(1357, \cdot)\) n/a 320 2
4788.2.bk \(\chi_{4788}(995, \cdot)\) n/a 1440 2
4788.2.bl \(\chi_{4788}(145, \cdot)\) n/a 132 2
4788.2.bm \(\chi_{4788}(3203, \cdot)\) n/a 640 2
4788.2.br \(\chi_{4788}(767, \cdot)\) n/a 1904 2
4788.2.bs \(\chi_{4788}(2497, \cdot)\) n/a 320 2
4788.2.bt \(\chi_{4788}(1661, \cdot)\) n/a 320 2
4788.2.bu \(\chi_{4788}(1375, \cdot)\) n/a 1904 2
4788.2.bz \(\chi_{4788}(2215, \cdot)\) n/a 792 2
4788.2.ca \(\chi_{4788}(2501, \cdot)\) n/a 104 2
4788.2.cb \(\chi_{4788}(1147, \cdot)\) n/a 1904 2
4788.2.cc \(\chi_{4788}(2801, \cdot)\) n/a 240 2
4788.2.cf \(\chi_{4788}(3685, \cdot)\) n/a 320 2
4788.2.cg \(\chi_{4788}(191, \cdot)\) n/a 1728 2
4788.2.cj \(\chi_{4788}(2839, \cdot)\) n/a 1904 2
4788.2.ck \(\chi_{4788}(425, \cdot)\) n/a 320 2
4788.2.cp \(\chi_{4788}(125, \cdot)\) n/a 112 2
4788.2.cq \(\chi_{4788}(3907, \cdot)\) n/a 600 2
4788.2.cr \(\chi_{4788}(331, \cdot)\) n/a 1904 2
4788.2.cs \(\chi_{4788}(2705, \cdot)\) n/a 320 2
4788.2.cz \(\chi_{4788}(227, \cdot)\) n/a 1904 2
4788.2.da \(\chi_{4788}(4511, \cdot)\) n/a 1904 2
4788.2.db \(\chi_{4788}(1595, \cdot)\) n/a 1904 2
4788.2.dc \(\chi_{4788}(2159, \cdot)\) n/a 640 2
4788.2.dl \(\chi_{4788}(2735, \cdot)\) n/a 640 2
4788.2.dm \(\chi_{4788}(335, \cdot)\) n/a 1904 2
4788.2.dn \(\chi_{4788}(1471, \cdot)\) n/a 1440 2
4788.2.do \(\chi_{4788}(2477, \cdot)\) n/a 320 2
4788.2.dp \(\chi_{4788}(1747, \cdot)\) n/a 792 2
4788.2.dq \(\chi_{4788}(2357, \cdot)\) 4788.2.dq.a 96 2
4788.2.dz \(\chi_{4788}(353, \cdot)\) n/a 320 2
4788.2.ea \(\chi_{4788}(2767, \cdot)\) n/a 1904 2
4788.2.eb \(\chi_{4788}(761, \cdot)\) n/a 288 2
4788.2.ec \(\chi_{4788}(151, \cdot)\) n/a 1904 2
4788.2.ed \(\chi_{4788}(487, \cdot)\) n/a 792 2
4788.2.ee \(\chi_{4788}(2861, \cdot)\) n/a 104 2
4788.2.ef \(\chi_{4788}(1975, \cdot)\) n/a 1440 2
4788.2.eg \(\chi_{4788}(1217, \cdot)\) n/a 288 2
4788.2.en \(\chi_{4788}(3527, \cdot)\) n/a 640 2
4788.2.eo \(\chi_{4788}(563, \cdot)\) n/a 1904 2
4788.2.et \(\chi_{4788}(1319, \cdot)\) n/a 1904 2
4788.2.eu \(\chi_{4788}(691, \cdot)\) n/a 1904 2
4788.2.ev \(\chi_{4788}(977, \cdot)\) n/a 320 2
4788.2.fa \(\chi_{4788}(4567, \cdot)\) n/a 1904 2
4788.2.fb \(\chi_{4788}(65, \cdot)\) n/a 320 2
4788.2.fc \(\chi_{4788}(449, \cdot)\) 4788.2.fc.a 40 2
4788.2.fc.b 40
4788.2.fd \(\chi_{4788}(3583, \cdot)\) n/a 792 2
4788.2.fk \(\chi_{4788}(265, \cdot)\) n/a 320 2
4788.2.fl \(\chi_{4788}(2927, \cdot)\) n/a 1296 2
4788.2.fm \(\chi_{4788}(829, \cdot)\) n/a 132 2
4788.2.fn \(\chi_{4788}(3887, \cdot)\) n/a 640 2
4788.2.fo \(\chi_{4788}(1787, \cdot)\) n/a 1728 2
4788.2.fp \(\chi_{4788}(493, \cdot)\) n/a 320 2
4788.2.fq \(\chi_{4788}(11, \cdot)\) n/a 1904 2
4788.2.fr \(\chi_{4788}(1741, \cdot)\) n/a 320 2
4788.2.ga \(\chi_{4788}(1405, \cdot)\) n/a 132 2
4788.2.gb \(\chi_{4788}(2699, \cdot)\) n/a 576 2
4788.2.gc \(\chi_{4788}(601, \cdot)\) n/a 320 2
4788.2.gd \(\chi_{4788}(239, \cdot)\) n/a 1440 2
4788.2.ge \(\chi_{4788}(391, \cdot)\) n/a 1904 2
4788.2.gf \(\chi_{4788}(2045, \cdot)\) n/a 240 2
4788.2.gg \(\chi_{4788}(1027, \cdot)\) n/a 720 2
4788.2.gh \(\chi_{4788}(3077, \cdot)\) n/a 104 2
4788.2.gq \(\chi_{4788}(1531, \cdot)\) n/a 792 2
4788.2.gr \(\chi_{4788}(1817, \cdot)\) n/a 104 2
4788.2.gs \(\chi_{4788}(1483, \cdot)\) n/a 1728 2
4788.2.gt \(\chi_{4788}(113, \cdot)\) n/a 240 2
4788.2.gu \(\chi_{4788}(905, \cdot)\) n/a 320 2
4788.2.gv \(\chi_{4788}(619, \cdot)\) n/a 1904 2
4788.2.gw \(\chi_{4788}(2165, \cdot)\) n/a 320 2
4788.2.gx \(\chi_{4788}(115, \cdot)\) n/a 1728 2
4788.2.he \(\chi_{4788}(2425, \cdot)\) n/a 320 2
4788.2.hf \(\chi_{4788}(695, \cdot)\) n/a 1904 2
4788.2.hg \(\chi_{4788}(1835, \cdot)\) n/a 480 2
4788.2.hh \(\chi_{4788}(2197, \cdot)\) n/a 136 2
4788.2.hm \(\chi_{4788}(3181, \cdot)\) n/a 320 2
4788.2.hn \(\chi_{4788}(1451, \cdot)\) n/a 1904 2
4788.2.hq \(\chi_{4788}(835, \cdot)\) n/a 1904 2
4788.2.hr \(\chi_{4788}(1445, \cdot)\) n/a 288 2
4788.2.hu \(\chi_{4788}(1475, \cdot)\) n/a 640 2
4788.2.hv \(\chi_{4788}(1091, \cdot)\) n/a 1904 2
4788.2.ia \(\chi_{4788}(635, \cdot)\) n/a 1904 2
4788.2.ib \(\chi_{4788}(1109, \cdot)\) n/a 320 2
4788.2.ic \(\chi_{4788}(3523, \cdot)\) n/a 1904 2
4788.2.ih \(\chi_{4788}(715, \cdot)\) n/a 1440 2
4788.2.ii \(\chi_{4788}(1721, \cdot)\) n/a 320 2
4788.2.ij \(\chi_{4788}(1171, \cdot)\) n/a 792 2
4788.2.ik \(\chi_{4788}(3545, \cdot)\) n/a 104 2
4788.2.in \(\chi_{4788}(1823, \cdot)\) n/a 1904 2
4788.2.iq \(\chi_{4788}(709, \cdot)\) n/a 960 6
4788.2.ir \(\chi_{4788}(25, \cdot)\) n/a 960 6
4788.2.is \(\chi_{4788}(253, \cdot)\) n/a 300 6
4788.2.it \(\chi_{4788}(85, \cdot)\) n/a 720 6
4788.2.iu \(\chi_{4788}(289, \cdot)\) n/a 402 6
4788.2.iv \(\chi_{4788}(1201, \cdot)\) n/a 960 6
4788.2.iw \(\chi_{4788}(1297, \cdot)\) n/a 402 6
4788.2.ix \(\chi_{4788}(529, \cdot)\) n/a 960 6
4788.2.iy \(\chi_{4788}(841, \cdot)\) n/a 720 6
4788.2.ja \(\chi_{4788}(29, \cdot)\) n/a 720 6
4788.2.jb \(\chi_{4788}(1469, \cdot)\) n/a 960 6
4788.2.jd \(\chi_{4788}(199, \cdot)\) n/a 2376 6
4788.2.je \(\chi_{4788}(859, \cdot)\) n/a 5712 6
4788.2.jj \(\chi_{4788}(751, \cdot)\) n/a 5712 6
4788.2.jk \(\chi_{4788}(667, \cdot)\) n/a 2376 6
4788.2.jn \(\chi_{4788}(1277, \cdot)\) n/a 324 6
4788.2.jo \(\chi_{4788}(605, \cdot)\) n/a 960 6
4788.2.jp \(\chi_{4788}(641, \cdot)\) n/a 960 6
4788.2.jq \(\chi_{4788}(53, \cdot)\) n/a 324 6
4788.2.jt \(\chi_{4788}(211, \cdot)\) n/a 4320 6
4788.2.jw \(\chi_{4788}(643, \cdot)\) n/a 5712 6
4788.2.jx \(\chi_{4788}(1619, \cdot)\) n/a 1920 6
4788.2.jy \(\chi_{4788}(947, \cdot)\) n/a 5712 6
4788.2.kd \(\chi_{4788}(299, \cdot)\) n/a 5712 6
4788.2.ke \(\chi_{4788}(1655, \cdot)\) n/a 1920 6
4788.2.kh \(\chi_{4788}(13, \cdot)\) n/a 960 6
4788.2.ki \(\chi_{4788}(181, \cdot)\) n/a 396 6
4788.2.kn \(\chi_{4788}(1321, \cdot)\) n/a 960 6
4788.2.ko \(\chi_{4788}(241, \cdot)\) n/a 960 6
4788.2.kr \(\chi_{4788}(167, \cdot)\) n/a 5712 6
4788.2.ks \(\chi_{4788}(755, \cdot)\) n/a 1920 6
4788.2.kx \(\chi_{4788}(1031, \cdot)\) n/a 5712 6
4788.2.ky \(\chi_{4788}(347, \cdot)\) n/a 5712 6
4788.2.kz \(\chi_{4788}(383, \cdot)\) n/a 5712 6
4788.2.la \(\chi_{4788}(59, \cdot)\) n/a 5712 6
4788.2.lf \(\chi_{4788}(575, \cdot)\) n/a 1440 6
4788.2.lg \(\chi_{4788}(2171, \cdot)\) n/a 4320 6
4788.2.lj \(\chi_{4788}(409, \cdot)\) n/a 960 6
4788.2.lk \(\chi_{4788}(325, \cdot)\) n/a 402 6
4788.2.ln \(\chi_{4788}(17, \cdot)\) n/a 324 6
4788.2.lo \(\chi_{4788}(929, \cdot)\) n/a 960 6
4788.2.lt \(\chi_{4788}(1229, \cdot)\) n/a 960 6
4788.2.lu \(\chi_{4788}(485, \cdot)\) n/a 324 6
4788.2.lx \(\chi_{4788}(1723, \cdot)\) n/a 4320 6
4788.2.ly \(\chi_{4788}(127, \cdot)\) n/a 1800 6
4788.2.lz \(\chi_{4788}(283, \cdot)\) n/a 5712 6
4788.2.ma \(\chi_{4788}(367, \cdot)\) n/a 5712 6
4788.2.mf \(\chi_{4788}(583, \cdot)\) n/a 5712 6
4788.2.mg \(\chi_{4788}(1663, \cdot)\) n/a 5712 6
4788.2.mh \(\chi_{4788}(55, \cdot)\) n/a 2376 6
4788.2.mi \(\chi_{4788}(139, \cdot)\) n/a 5712 6
4788.2.ml \(\chi_{4788}(1541, \cdot)\) n/a 720 6
4788.2.mm \(\chi_{4788}(953, \cdot)\) n/a 240 6
4788.2.mr \(\chi_{4788}(5, \cdot)\) n/a 960 6
4788.2.ms \(\chi_{4788}(689, \cdot)\) n/a 960 6
4788.2.mt \(\chi_{4788}(401, \cdot)\) n/a 960 6
4788.2.mu \(\chi_{4788}(317, \cdot)\) n/a 960 6
4788.2.mz \(\chi_{4788}(377, \cdot)\) n/a 312 6
4788.2.na \(\chi_{4788}(461, \cdot)\) n/a 960 6
4788.2.nd \(\chi_{4788}(955, \cdot)\) n/a 2376 6
4788.2.ne \(\chi_{4788}(187, \cdot)\) n/a 5712 6
4788.2.nf \(\chi_{4788}(67, \cdot)\) n/a 5712 6
4788.2.ng \(\chi_{4788}(991, \cdot)\) n/a 2376 6
4788.2.nk \(\chi_{4788}(1343, \cdot)\) n/a 5712 6
4788.2.nl \(\chi_{4788}(491, \cdot)\) n/a 4320 6
4788.2.nr \(\chi_{4788}(1249, \cdot)\) n/a 960 6
4788.2.ns \(\chi_{4788}(649, \cdot)\) n/a 402 6
4788.2.nv \(\chi_{4788}(359, \cdot)\) n/a 1920 6
4788.2.nw \(\chi_{4788}(23, \cdot)\) n/a 5712 6
4788.2.nx \(\chi_{4788}(887, \cdot)\) n/a 5712 6
4788.2.ny \(\chi_{4788}(143, \cdot)\) n/a 1920 6
4788.2.ob \(\chi_{4788}(1021, \cdot)\) n/a 960 6

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4788))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4788)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(63))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(84))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(126))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(133))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(252))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(266))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(399))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(532))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(798))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1197))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1596))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2394))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4788))\)\(^{\oplus 1}\)