Properties

Label 4680.2
Level 4680
Weight 2
Dimension 232996
Nonzero newspaces 150
Sturm bound 2322432

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Defining parameters

Level: \( N \) = \( 4680 = 2^{3} \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 150 \)
Sturm bound: \(2322432\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(4680))\).

Total New Old
Modular forms 589824 235372 354452
Cusp forms 571393 232996 338397
Eisenstein series 18431 2376 16055

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(4680))\)

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
4680.2.a \(\chi_{4680}(1, \cdot)\) 4680.2.a.a 1 1
4680.2.a.b 1
4680.2.a.c 1
4680.2.a.d 1
4680.2.a.e 1
4680.2.a.f 1
4680.2.a.g 1
4680.2.a.h 1
4680.2.a.i 1
4680.2.a.j 1
4680.2.a.k 1
4680.2.a.l 1
4680.2.a.m 1
4680.2.a.n 1
4680.2.a.o 1
4680.2.a.p 1
4680.2.a.q 1
4680.2.a.r 1
4680.2.a.s 1
4680.2.a.t 1
4680.2.a.u 1
4680.2.a.v 1
4680.2.a.w 2
4680.2.a.x 2
4680.2.a.y 2
4680.2.a.z 2
4680.2.a.ba 2
4680.2.a.bb 2
4680.2.a.bc 2
4680.2.a.bd 2
4680.2.a.be 2
4680.2.a.bf 2
4680.2.a.bg 3
4680.2.a.bh 3
4680.2.a.bi 3
4680.2.a.bj 3
4680.2.a.bk 3
4680.2.a.bl 3
4680.2.b \(\chi_{4680}(469, \cdot)\) n/a 360 1
4680.2.e \(\chi_{4680}(1691, \cdot)\) n/a 192 1
4680.2.g \(\chi_{4680}(2521, \cdot)\) 4680.2.g.a 2 1
4680.2.g.b 2
4680.2.g.c 2
4680.2.g.d 2
4680.2.g.e 2
4680.2.g.f 4
4680.2.g.g 4
4680.2.g.h 4
4680.2.g.i 6
4680.2.g.j 6
4680.2.g.k 8
4680.2.g.l 12
4680.2.g.m 16
4680.2.h \(\chi_{4680}(4679, \cdot)\) None 0 1
4680.2.k \(\chi_{4680}(4031, \cdot)\) None 0 1
4680.2.l \(\chi_{4680}(2809, \cdot)\) 4680.2.l.a 2 1
4680.2.l.b 2
4680.2.l.c 2
4680.2.l.d 6
4680.2.l.e 6
4680.2.l.f 8
4680.2.l.g 8
4680.2.l.h 10
4680.2.l.i 10
4680.2.l.j 18
4680.2.l.k 18
4680.2.n \(\chi_{4680}(2339, \cdot)\) n/a 336 1
4680.2.q \(\chi_{4680}(181, \cdot)\) n/a 280 1
4680.2.r \(\chi_{4680}(649, \cdot)\) n/a 104 1
4680.2.u \(\chi_{4680}(1871, \cdot)\) None 0 1
4680.2.w \(\chi_{4680}(2341, \cdot)\) n/a 240 1
4680.2.x \(\chi_{4680}(4499, \cdot)\) n/a 288 1
4680.2.ba \(\chi_{4680}(4211, \cdot)\) n/a 224 1
4680.2.bb \(\chi_{4680}(2989, \cdot)\) n/a 416 1
4680.2.bd \(\chi_{4680}(2159, \cdot)\) None 0 1
4680.2.bg \(\chi_{4680}(2161, \cdot)\) n/a 140 2
4680.2.bh \(\chi_{4680}(1561, \cdot)\) n/a 288 2
4680.2.bi \(\chi_{4680}(601, \cdot)\) n/a 336 2
4680.2.bj \(\chi_{4680}(2401, \cdot)\) n/a 336 2
4680.2.bk \(\chi_{4680}(73, \cdot)\) n/a 210 2
4680.2.bl \(\chi_{4680}(827, \cdot)\) n/a 672 2
4680.2.bq \(\chi_{4680}(2413, \cdot)\) n/a 832 2
4680.2.br \(\chi_{4680}(863, \cdot)\) None 0 2
4680.2.bt \(\chi_{4680}(1637, \cdot)\) n/a 672 2
4680.2.bu \(\chi_{4680}(1457, \cdot)\) n/a 144 2
4680.2.bx \(\chi_{4680}(703, \cdot)\) None 0 2
4680.2.by \(\chi_{4680}(883, \cdot)\) n/a 832 2
4680.2.cb \(\chi_{4680}(1529, \cdot)\) n/a 168 2
4680.2.cc \(\chi_{4680}(629, \cdot)\) n/a 672 2
4680.2.ce \(\chi_{4680}(811, \cdot)\) n/a 560 2
4680.2.ch \(\chi_{4680}(1711, \cdot)\) None 0 2
4680.2.cj \(\chi_{4680}(2179, \cdot)\) n/a 832 2
4680.2.ck \(\chi_{4680}(1279, \cdot)\) None 0 2
4680.2.cm \(\chi_{4680}(161, \cdot)\) n/a 112 2
4680.2.cp \(\chi_{4680}(1061, \cdot)\) n/a 448 2
4680.2.cq \(\chi_{4680}(2287, \cdot)\) None 0 2
4680.2.ct \(\chi_{4680}(2107, \cdot)\) n/a 720 2
4680.2.cu \(\chi_{4680}(53, \cdot)\) n/a 576 2
4680.2.cx \(\chi_{4680}(233, \cdot)\) n/a 168 2
4680.2.da \(\chi_{4680}(1763, \cdot)\) n/a 672 2
4680.2.db \(\chi_{4680}(1513, \cdot)\) n/a 210 2
4680.2.dc \(\chi_{4680}(4103, \cdot)\) None 0 2
4680.2.dd \(\chi_{4680}(1477, \cdot)\) n/a 832 2
4680.2.dh \(\chi_{4680}(4021, \cdot)\) n/a 1344 2
4680.2.di \(\chi_{4680}(3299, \cdot)\) n/a 2000 2
4680.2.dk \(\chi_{4680}(529, \cdot)\) n/a 504 2
4680.2.dn \(\chi_{4680}(191, \cdot)\) None 0 2
4680.2.do \(\chi_{4680}(959, \cdot)\) None 0 2
4680.2.dr \(\chi_{4680}(1681, \cdot)\) n/a 336 2
4680.2.dt \(\chi_{4680}(2291, \cdot)\) n/a 1344 2
4680.2.du \(\chi_{4680}(2869, \cdot)\) n/a 2000 2
4680.2.dx \(\chi_{4680}(2219, \cdot)\) n/a 2000 2
4680.2.dy \(\chi_{4680}(2941, \cdot)\) n/a 1344 2
4680.2.ea \(\chi_{4680}(1031, \cdot)\) None 0 2
4680.2.ed \(\chi_{4680}(1609, \cdot)\) n/a 504 2
4680.2.ee \(\chi_{4680}(1091, \cdot)\) n/a 1344 2
4680.2.eh \(\chi_{4680}(1429, \cdot)\) n/a 2000 2
4680.2.ek \(\chi_{4680}(1439, \cdot)\) None 0 2
4680.2.em \(\chi_{4680}(829, \cdot)\) n/a 832 2
4680.2.en \(\chi_{4680}(251, \cdot)\) n/a 448 2
4680.2.eq \(\chi_{4680}(599, \cdot)\) None 0 2
4680.2.et \(\chi_{4680}(2209, \cdot)\) n/a 504 2
4680.2.eu \(\chi_{4680}(311, \cdot)\) None 0 2
4680.2.ex \(\chi_{4680}(1979, \cdot)\) n/a 672 2
4680.2.ey \(\chi_{4680}(1621, \cdot)\) n/a 560 2
4680.2.fa \(\chi_{4680}(2591, \cdot)\) None 0 2
4680.2.fd \(\chi_{4680}(1369, \cdot)\) n/a 208 2
4680.2.fe \(\chi_{4680}(781, \cdot)\) n/a 1152 2
4680.2.fh \(\chi_{4680}(1379, \cdot)\) n/a 1728 2
4680.2.fk \(\chi_{4680}(1199, \cdot)\) None 0 2
4680.2.fm \(\chi_{4680}(589, \cdot)\) n/a 2000 2
4680.2.fn \(\chi_{4680}(3371, \cdot)\) n/a 1344 2
4680.2.fq \(\chi_{4680}(3839, \cdot)\) None 0 2
4680.2.fr \(\chi_{4680}(121, \cdot)\) n/a 336 2
4680.2.ft \(\chi_{4680}(731, \cdot)\) n/a 1344 2
4680.2.fw \(\chi_{4680}(1069, \cdot)\) n/a 2000 2
4680.2.fx \(\chi_{4680}(911, \cdot)\) None 0 2
4680.2.ga \(\chi_{4680}(1249, \cdot)\) n/a 432 2
4680.2.gb \(\chi_{4680}(901, \cdot)\) n/a 560 2
4680.2.ge \(\chi_{4680}(179, \cdot)\) n/a 672 2
4680.2.gg \(\chi_{4680}(289, \cdot)\) n/a 212 2
4680.2.gh \(\chi_{4680}(1511, \cdot)\) None 0 2
4680.2.gk \(\chi_{4680}(779, \cdot)\) n/a 2000 2
4680.2.gl \(\chi_{4680}(1741, \cdot)\) n/a 1344 2
4680.2.go \(\chi_{4680}(2029, \cdot)\) n/a 1728 2
4680.2.gp \(\chi_{4680}(131, \cdot)\) n/a 1152 2
4680.2.gs \(\chi_{4680}(719, \cdot)\) None 0 2
4680.2.gt \(\chi_{4680}(361, \cdot)\) n/a 140 2
4680.2.gv \(\chi_{4680}(971, \cdot)\) n/a 448 2
4680.2.gy \(\chi_{4680}(2629, \cdot)\) n/a 832 2
4680.2.gz \(\chi_{4680}(961, \cdot)\) n/a 336 2
4680.2.hc \(\chi_{4680}(1559, \cdot)\) None 0 2
4680.2.hd \(\chi_{4680}(1141, \cdot)\) n/a 1344 2
4680.2.hg \(\chi_{4680}(1499, \cdot)\) n/a 2000 2
4680.2.hi \(\chi_{4680}(3409, \cdot)\) n/a 504 2
4680.2.hj \(\chi_{4680}(1751, \cdot)\) None 0 2
4680.2.hm \(\chi_{4680}(2759, \cdot)\) None 0 2
4680.2.ho \(\chi_{4680}(2149, \cdot)\) n/a 2000 2
4680.2.hr \(\chi_{4680}(491, \cdot)\) n/a 1344 2
4680.2.hs \(\chi_{4680}(419, \cdot)\) n/a 2000 2
4680.2.hv \(\chi_{4680}(61, \cdot)\) n/a 1344 2
4680.2.hx \(\chi_{4680}(2831, \cdot)\) None 0 2
4680.2.hy \(\chi_{4680}(49, \cdot)\) n/a 504 2
4680.2.ia \(\chi_{4680}(167, \cdot)\) None 0 4
4680.2.ib \(\chi_{4680}(1237, \cdot)\) n/a 4000 4
4680.2.ig \(\chi_{4680}(1163, \cdot)\) n/a 4000 4
4680.2.ih \(\chi_{4680}(97, \cdot)\) n/a 1008 4
4680.2.ii \(\chi_{4680}(817, \cdot)\) n/a 1008 4
4680.2.ij \(\chi_{4680}(587, \cdot)\) n/a 4000 4
4680.2.im \(\chi_{4680}(733, \cdot)\) n/a 4000 4
4680.2.in \(\chi_{4680}(983, \cdot)\) None 0 4
4680.2.iq \(\chi_{4680}(1007, \cdot)\) None 0 4
4680.2.ir \(\chi_{4680}(37, \cdot)\) n/a 1664 4
4680.2.iw \(\chi_{4680}(323, \cdot)\) n/a 1344 4
4680.2.ix \(\chi_{4680}(2377, \cdot)\) n/a 420 4
4680.2.ja \(\chi_{4680}(697, \cdot)\) n/a 1008 4
4680.2.jb \(\chi_{4680}(203, \cdot)\) n/a 4000 4
4680.2.je \(\chi_{4680}(1813, \cdot)\) n/a 4000 4
4680.2.jf \(\chi_{4680}(1463, \cdot)\) None 0 4
4680.2.jg \(\chi_{4680}(367, \cdot)\) None 0 4
4680.2.jj \(\chi_{4680}(907, \cdot)\) n/a 4000 4
4680.2.jk \(\chi_{4680}(797, \cdot)\) n/a 4000 4
4680.2.jn \(\chi_{4680}(113, \cdot)\) n/a 1008 4
4680.2.jo \(\chi_{4680}(547, \cdot)\) n/a 3456 4
4680.2.jr \(\chi_{4680}(103, \cdot)\) None 0 4
4680.2.js \(\chi_{4680}(17, \cdot)\) n/a 336 4
4680.2.jv \(\chi_{4680}(257, \cdot)\) n/a 1008 4
4680.2.jw \(\chi_{4680}(653, \cdot)\) n/a 4000 4
4680.2.jz \(\chi_{4680}(1277, \cdot)\) n/a 1344 4
4680.2.ka \(\chi_{4680}(523, \cdot)\) n/a 1664 4
4680.2.kd \(\chi_{4680}(763, \cdot)\) n/a 4000 4
4680.2.ke \(\chi_{4680}(1447, \cdot)\) None 0 4
4680.2.kh \(\chi_{4680}(127, \cdot)\) None 0 4
4680.2.ki \(\chi_{4680}(857, \cdot)\) n/a 1008 4
4680.2.kl \(\chi_{4680}(677, \cdot)\) n/a 3456 4
4680.2.kn \(\chi_{4680}(31, \cdot)\) None 0 4
4680.2.ko \(\chi_{4680}(931, \cdot)\) n/a 2688 4
4680.2.kq \(\chi_{4680}(749, \cdot)\) n/a 4000 4
4680.2.kt \(\chi_{4680}(1409, \cdot)\) n/a 1008 4
4680.2.ku \(\chi_{4680}(799, \cdot)\) None 0 4
4680.2.kx \(\chi_{4680}(1939, \cdot)\) n/a 4000 4
4680.2.ky \(\chi_{4680}(761, \cdot)\) n/a 672 4
4680.2.lb \(\chi_{4680}(3581, \cdot)\) n/a 896 4
4680.2.lc \(\chi_{4680}(1241, \cdot)\) n/a 224 4
4680.2.lf \(\chi_{4680}(821, \cdot)\) n/a 2688 4
4680.2.lh \(\chi_{4680}(1579, \cdot)\) n/a 4000 4
4680.2.li \(\chi_{4680}(2359, \cdot)\) None 0 4
4680.2.ll \(\chi_{4680}(19, \cdot)\) n/a 1664 4
4680.2.lm \(\chi_{4680}(319, \cdot)\) None 0 4
4680.2.lp \(\chi_{4680}(461, \cdot)\) n/a 2688 4
4680.2.lq \(\chi_{4680}(41, \cdot)\) n/a 672 4
4680.2.ls \(\chi_{4680}(509, \cdot)\) n/a 4000 4
4680.2.lv \(\chi_{4680}(929, \cdot)\) n/a 1008 4
4680.2.lw \(\chi_{4680}(691, \cdot)\) n/a 2688 4
4680.2.lz \(\chi_{4680}(271, \cdot)\) None 0 4
4680.2.ma \(\chi_{4680}(1891, \cdot)\) n/a 1120 4
4680.2.md \(\chi_{4680}(1111, \cdot)\) None 0 4
4680.2.mf \(\chi_{4680}(1289, \cdot)\) n/a 1008 4
4680.2.mg \(\chi_{4680}(1709, \cdot)\) n/a 1344 4
4680.2.mj \(\chi_{4680}(89, \cdot)\) n/a 336 4
4680.2.mk \(\chi_{4680}(149, \cdot)\) n/a 4000 4
4680.2.mn \(\chi_{4680}(1471, \cdot)\) None 0 4
4680.2.mo \(\chi_{4680}(331, \cdot)\) n/a 2688 4
4680.2.mr \(\chi_{4680}(941, \cdot)\) n/a 2688 4
4680.2.ms \(\chi_{4680}(281, \cdot)\) n/a 672 4
4680.2.mu \(\chi_{4680}(1399, \cdot)\) None 0 4
4680.2.mx \(\chi_{4680}(499, \cdot)\) n/a 4000 4
4680.2.mz \(\chi_{4680}(833, \cdot)\) n/a 864 4
4680.2.na \(\chi_{4680}(77, \cdot)\) n/a 4000 4
4680.2.nc \(\chi_{4680}(43, \cdot)\) n/a 4000 4
4680.2.nf \(\chi_{4680}(667, \cdot)\) n/a 1664 4
4680.2.ng \(\chi_{4680}(1927, \cdot)\) None 0 4
4680.2.nj \(\chi_{4680}(2167, \cdot)\) None 0 4
4680.2.nk \(\chi_{4680}(2057, \cdot)\) n/a 1008 4
4680.2.nn \(\chi_{4680}(737, \cdot)\) n/a 336 4
4680.2.no \(\chi_{4680}(413, \cdot)\) n/a 1344 4
4680.2.nr \(\chi_{4680}(173, \cdot)\) n/a 4000 4
4680.2.nt \(\chi_{4680}(1507, \cdot)\) n/a 4000 4
4680.2.nu \(\chi_{4680}(1327, \cdot)\) None 0 4
4680.2.nx \(\chi_{4680}(1517, \cdot)\) n/a 4000 4
4680.2.ny \(\chi_{4680}(3137, \cdot)\) n/a 1008 4
4680.2.ob \(\chi_{4680}(823, \cdot)\) None 0 4
4680.2.oc \(\chi_{4680}(2707, \cdot)\) n/a 4000 4
4680.2.og \(\chi_{4680}(947, \cdot)\) n/a 4000 4
4680.2.oh \(\chi_{4680}(457, \cdot)\) n/a 1008 4
4680.2.ok \(\chi_{4680}(973, \cdot)\) n/a 1664 4
4680.2.ol \(\chi_{4680}(1727, \cdot)\) None 0 4
4680.2.oo \(\chi_{4680}(47, \cdot)\) None 0 4
4680.2.op \(\chi_{4680}(853, \cdot)\) n/a 4000 4
4680.2.oq \(\chi_{4680}(83, \cdot)\) n/a 4000 4
4680.2.or \(\chi_{4680}(1633, \cdot)\) n/a 1008 4
4680.2.ou \(\chi_{4680}(1657, \cdot)\) n/a 420 4
4680.2.ov \(\chi_{4680}(4067, \cdot)\) n/a 1344 4
4680.2.oy \(\chi_{4680}(383, \cdot)\) None 0 4
4680.2.oz \(\chi_{4680}(877, \cdot)\) n/a 4000 4
4680.2.pe \(\chi_{4680}(1597, \cdot)\) n/a 4000 4
4680.2.pf \(\chi_{4680}(1103, \cdot)\) None 0 4
4680.2.pg \(\chi_{4680}(1033, \cdot)\) n/a 1008 4
4680.2.ph \(\chi_{4680}(227, \cdot)\) n/a 4000 4

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(4680))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(4680)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(52))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(104))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(120))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(156))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(180))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(260))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(312))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(360))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(468))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(520))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(780))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(936))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1170))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1560))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2340))\)\(^{\oplus 2}\)