Properties

 Label 4641.2 Level 4641 Weight 2 Dimension 542665 Nonzero newspaces 180 Sturm bound 3096576

Defining parameters

 Level: $$N$$ = $$4641 = 3 \cdot 7 \cdot 13 \cdot 17$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$180$$ Sturm bound: $$3096576$$

Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(4641))$$.

Total New Old
Modular forms 783360 549273 234087
Cusp forms 764929 542665 222264
Eisenstein series 18431 6608 11823

Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(4641))$$

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
4641.2.a $$\chi_{4641}(1, \cdot)$$ 4641.2.a.a 1 1
4641.2.a.b 1
4641.2.a.c 1
4641.2.a.d 1
4641.2.a.e 1
4641.2.a.f 1
4641.2.a.g 1
4641.2.a.h 2
4641.2.a.i 2
4641.2.a.j 2
4641.2.a.k 2
4641.2.a.l 7
4641.2.a.m 7
4641.2.a.n 7
4641.2.a.o 8
4641.2.a.p 9
4641.2.a.q 9
4641.2.a.r 9
4641.2.a.s 11
4641.2.a.t 12
4641.2.a.u 12
4641.2.a.v 13
4641.2.a.w 14
4641.2.a.x 14
4641.2.a.y 14
4641.2.a.z 15
4641.2.a.ba 17
4641.2.b $$\chi_{4641}(1429, \cdot)$$ n/a 224 1
4641.2.d $$\chi_{4641}(3212, \cdot)$$ n/a 576 1
4641.2.f $$\chi_{4641}(3758, \cdot)$$ n/a 512 1
4641.2.h $$\chi_{4641}(883, \cdot)$$ n/a 256 1
4641.2.k $$\chi_{4641}(4096, \cdot)$$ n/a 216 1
4641.2.m $$\chi_{4641}(545, \cdot)$$ n/a 600 1
4641.2.o $$\chi_{4641}(4640, \cdot)$$ n/a 664 1
4641.2.q $$\chi_{4641}(1327, \cdot)$$ n/a 512 2
4641.2.r $$\chi_{4641}(919, \cdot)$$ n/a 596 2
4641.2.s $$\chi_{4641}(3214, \cdot)$$ n/a 448 2
4641.2.t $$\chi_{4641}(256, \cdot)$$ n/a 596 2
4641.2.u $$\chi_{4641}(1364, \cdot)$$ n/a 1328 2
4641.2.v $$\chi_{4641}(820, \cdot)$$ n/a 432 2
4641.2.z $$\chi_{4641}(3515, \cdot)$$ n/a 1008 2
4641.2.ba $$\chi_{4641}(1084, \cdot)$$ n/a 672 2
4641.2.bd $$\chi_{4641}(1903, \cdot)$$ n/a 672 2
4641.2.bf $$\chi_{4641}(239, \cdot)$$ n/a 896 2
4641.2.bg $$\chi_{4641}(2192, \cdot)$$ n/a 1008 2
4641.2.bi $$\chi_{4641}(307, \cdot)$$ n/a 592 2
4641.2.bl $$\chi_{4641}(3268, \cdot)$$ n/a 672 2
4641.2.bm $$\chi_{4641}(1058, \cdot)$$ n/a 1008 2
4641.2.bq $$\chi_{4641}(64, \cdot)$$ n/a 512 2
4641.2.br $$\chi_{4641}(2393, \cdot)$$ n/a 1152 2
4641.2.bt $$\chi_{4641}(3280, \cdot)$$ n/a 672 2
4641.2.bv $$\chi_{4641}(341, \cdot)$$ n/a 1196 2
4641.2.bx $$\chi_{4641}(815, \cdot)$$ n/a 1328 2
4641.2.bz $$\chi_{4641}(205, \cdot)$$ n/a 596 2
4641.2.ca $$\chi_{4641}(1616, \cdot)$$ n/a 1192 2
4641.2.cc $$\chi_{4641}(2668, \cdot)$$ n/a 496 2
4641.2.cf $$\chi_{4641}(2651, \cdot)$$ n/a 1328 2
4641.2.ci $$\chi_{4641}(101, \cdot)$$ n/a 1328 2
4641.2.cl $$\chi_{4641}(373, \cdot)$$ n/a 672 2
4641.2.cn $$\chi_{4641}(647, \cdot)$$ n/a 1196 2
4641.2.co $$\chi_{4641}(3197, \cdot)$$ n/a 1192 2
4641.2.cq $$\chi_{4641}(781, \cdot)$$ n/a 576 2
4641.2.ct $$\chi_{4641}(1070, \cdot)$$ n/a 1328 2
4641.2.cw $$\chi_{4641}(1784, \cdot)$$ n/a 1328 2
4641.2.cy $$\chi_{4641}(2500, \cdot)$$ n/a 448 2
4641.2.cz $$\chi_{4641}(698, \cdot)$$ n/a 1196 2
4641.2.db $$\chi_{4641}(3637, \cdot)$$ n/a 672 2
4641.2.de $$\chi_{4641}(2209, \cdot)$$ n/a 672 2
4641.2.dg $$\chi_{4641}(1769, \cdot)$$ n/a 1024 2
4641.2.di $$\chi_{4641}(1223, \cdot)$$ n/a 1152 2
4641.2.dk $$\chi_{4641}(2755, \cdot)$$ n/a 600 2
4641.2.dl $$\chi_{4641}(4183, \cdot)$$ n/a 596 2
4641.2.dn $$\chi_{4641}(152, \cdot)$$ n/a 1328 2
4641.2.dq $$\chi_{4641}(1954, \cdot)$$ n/a 512 2
4641.2.ds $$\chi_{4641}(2330, \cdot)$$ n/a 1192 2
4641.2.du $$\chi_{4641}(4079, \cdot)$$ n/a 1328 2
4641.2.dw $$\chi_{4641}(290, \cdot)$$ n/a 1196 2
4641.2.dy $$\chi_{4641}(16, \cdot)$$ n/a 672 2
4641.2.ec $$\chi_{4641}(8, \cdot)$$ n/a 2016 4
4641.2.ed $$\chi_{4641}(580, \cdot)$$ n/a 1344 4
4641.2.ee $$\chi_{4641}(1028, \cdot)$$ n/a 2304 4
4641.2.ef $$\chi_{4641}(274, \cdot)$$ n/a 864 4
4641.2.eg $$\chi_{4641}(610, \cdot)$$ n/a 992 4
4641.2.eh $$\chi_{4641}(818, \cdot)$$ n/a 2656 4
4641.2.em $$\chi_{4641}(1919, \cdot)$$ n/a 2016 4
4641.2.en $$\chi_{4641}(1630, \cdot)$$ n/a 1344 4
4641.2.es $$\chi_{4641}(1075, \cdot)$$ n/a 1344 4
4641.2.et $$\chi_{4641}(803, \cdot)$$ n/a 2656 4
4641.2.ew $$\chi_{4641}(1135, \cdot)$$ n/a 1024 4
4641.2.ex $$\chi_{4641}(965, \cdot)$$ n/a 2656 4
4641.2.ey $$\chi_{4641}(404, \cdot)$$ n/a 2304 4
4641.2.ez $$\chi_{4641}(1390, \cdot)$$ n/a 1344 4
4641.2.fe $$\chi_{4641}(1517, \cdot)$$ n/a 2656 4
4641.2.ff $$\chi_{4641}(361, \cdot)$$ n/a 1344 4
4641.2.fh $$\chi_{4641}(548, \cdot)$$ n/a 2656 4
4641.2.fi $$\chi_{4641}(1228, \cdot)$$ n/a 1344 4
4641.2.fk $$\chi_{4641}(409, \cdot)$$ n/a 1192 4
4641.2.fm $$\chi_{4641}(305, \cdot)$$ n/a 2656 4
4641.2.fp $$\chi_{4641}(137, \cdot)$$ n/a 2392 4
4641.2.fr $$\chi_{4641}(271, \cdot)$$ n/a 1344 4
4641.2.ft $$\chi_{4641}(514, \cdot)$$ n/a 1344 4
4641.2.fu $$\chi_{4641}(956, \cdot)$$ n/a 2656 4
4641.2.fw $$\chi_{4641}(370, \cdot)$$ n/a 1344 4
4641.2.fz $$\chi_{4641}(1016, \cdot)$$ n/a 2016 4
4641.2.ga $$\chi_{4641}(115, \cdot)$$ n/a 1344 4
4641.2.gd $$\chi_{4641}(2384, \cdot)$$ n/a 2656 4
4641.2.ge $$\chi_{4641}(1279, \cdot)$$ n/a 1344 4
4641.2.gh $$\chi_{4641}(557, \cdot)$$ n/a 2656 4
4641.2.gi $$\chi_{4641}(800, \cdot)$$ n/a 2392 4
4641.2.gk $$\chi_{4641}(934, \cdot)$$ n/a 1344 4
4641.2.gn $$\chi_{4641}(1019, \cdot)$$ n/a 2656 4
4641.2.gp $$\chi_{4641}(1021, \cdot)$$ n/a 1200 4
4641.2.gr $$\chi_{4641}(50, \cdot)$$ n/a 2016 4
4641.2.gt $$\chi_{4641}(460, \cdot)$$ n/a 1200 4
4641.2.gu $$\chi_{4641}(577, \cdot)$$ n/a 1344 4
4641.2.gw $$\chi_{4641}(596, \cdot)$$ n/a 1792 4
4641.2.gy $$\chi_{4641}(475, \cdot)$$ n/a 1344 4
4641.2.ha $$\chi_{4641}(86, \cdot)$$ n/a 2384 4
4641.2.hd $$\chi_{4641}(1480, \cdot)$$ n/a 1192 4
4641.2.hf $$\chi_{4641}(254, \cdot)$$ n/a 2656 4
4641.2.hg $$\chi_{4641}(149, \cdot)$$ n/a 2656 4
4641.2.hj $$\chi_{4641}(3736, \cdot)$$ n/a 1344 4
4641.2.hk $$\chi_{4641}(200, \cdot)$$ n/a 2656 4
4641.2.hn $$\chi_{4641}(1900, \cdot)$$ n/a 1344 4
4641.2.ho $$\chi_{4641}(344, \cdot)$$ n/a 2016 4
4641.2.hr $$\chi_{4641}(769, \cdot)$$ n/a 1344 4
4641.2.hs $$\chi_{4641}(718, \cdot)$$ n/a 1344 4
4641.2.ht $$\chi_{4641}(446, \cdot)$$ n/a 2656 4
4641.2.hy $$\chi_{4641}(251, \cdot)$$ n/a 2656 4
4641.2.hz $$\chi_{4641}(1849, \cdot)$$ n/a 992 4
4641.2.ia $$\chi_{4641}(625, \cdot)$$ n/a 1152 4
4641.2.ib $$\chi_{4641}(38, \cdot)$$ n/a 2656 4
4641.2.ie $$\chi_{4641}(1160, \cdot)$$ n/a 2656 4
4641.2.if $$\chi_{4641}(4, \cdot)$$ n/a 1344 4
4641.2.ik $$\chi_{4641}(148, \cdot)$$ n/a 2016 8
4641.2.il $$\chi_{4641}(125, \cdot)$$ n/a 5312 8
4641.2.in $$\chi_{4641}(1210, \cdot)$$ n/a 2304 8
4641.2.ip $$\chi_{4641}(428, \cdot)$$ n/a 4032 8
4641.2.ir $$\chi_{4641}(92, \cdot)$$ n/a 3456 8
4641.2.it $$\chi_{4641}(181, \cdot)$$ n/a 2688 8
4641.2.iw $$\chi_{4641}(190, \cdot)$$ n/a 2016 8
4641.2.ix $$\chi_{4641}(1763, \cdot)$$ n/a 5312 8
4641.2.iy $$\chi_{4641}(145, \cdot)$$ n/a 2688 8
4641.2.iz $$\chi_{4641}(2, \cdot)$$ n/a 5312 8
4641.2.jc $$\chi_{4641}(19, \cdot)$$ n/a 2688 8
4641.2.jd $$\chi_{4641}(977, \cdot)$$ n/a 5312 8
4641.2.ji $$\chi_{4641}(76, \cdot)$$ n/a 2688 8
4641.2.jj $$\chi_{4641}(869, \cdot)$$ n/a 4032 8
4641.2.jk $$\chi_{4641}(359, \cdot)$$ n/a 5312 8
4641.2.jl $$\chi_{4641}(229, \cdot)$$ n/a 2688 8
4641.2.js $$\chi_{4641}(257, \cdot)$$ n/a 5312 8
4641.2.jt $$\chi_{4641}(478, \cdot)$$ n/a 2688 8
4641.2.ju $$\chi_{4641}(529, \cdot)$$ n/a 2688 8
4641.2.jv $$\chi_{4641}(542, \cdot)$$ n/a 5312 8
4641.2.jw $$\chi_{4641}(484, \cdot)$$ n/a 2048 8
4641.2.jx $$\chi_{4641}(230, \cdot)$$ n/a 5312 8
4641.2.jy $$\chi_{4641}(797, \cdot)$$ n/a 5312 8
4641.2.jz $$\chi_{4641}(43, \cdot)$$ n/a 1984 8
4641.2.ki $$\chi_{4641}(25, \cdot)$$ n/a 2688 8
4641.2.kj $$\chi_{4641}(920, \cdot)$$ n/a 5312 8
4641.2.kk $$\chi_{4641}(121, \cdot)$$ n/a 2688 8
4641.2.kl $$\chi_{4641}(467, \cdot)$$ n/a 5312 8
4641.2.km $$\chi_{4641}(950, \cdot)$$ n/a 4608 8
4641.2.kn $$\chi_{4641}(100, \cdot)$$ n/a 2688 8
4641.2.ko $$\chi_{4641}(185, \cdot)$$ n/a 5312 8
4641.2.kp $$\chi_{4641}(508, \cdot)$$ n/a 2304 8
4641.2.kw $$\chi_{4641}(202, \cdot)$$ n/a 2688 8
4641.2.kx $$\chi_{4641}(722, \cdot)$$ n/a 4032 8
4641.2.ky $$\chi_{4641}(746, \cdot)$$ n/a 5312 8
4641.2.kz $$\chi_{4641}(2140, \cdot)$$ n/a 2688 8
4641.2.le $$\chi_{4641}(535, \cdot)$$ n/a 2688 8
4641.2.lf $$\chi_{4641}(695, \cdot)$$ n/a 5312 8
4641.2.li $$\chi_{4641}(682, \cdot)$$ n/a 2688 8
4641.2.lj $$\chi_{4641}(410, \cdot)$$ n/a 5312 8
4641.2.lk $$\chi_{4641}(227, \cdot)$$ n/a 10624 16
4641.2.ll $$\chi_{4641}(37, \cdot)$$ n/a 5376 16
4641.2.lo $$\chi_{4641}(199, \cdot)$$ n/a 5376 16
4641.2.lq $$\chi_{4641}(74, \cdot)$$ n/a 10624 16
4641.2.ls $$\chi_{4641}(23, \cdot)$$ n/a 10624 16
4641.2.lu $$\chi_{4641}(250, \cdot)$$ n/a 5376 16
4641.2.lw $$\chi_{4641}(605, \cdot)$$ n/a 10624 16
4641.2.lx $$\chi_{4641}(184, \cdot)$$ n/a 5376 16
4641.2.ma $$\chi_{4641}(232, \cdot)$$ n/a 4032 16
4641.2.mb $$\chi_{4641}(734, \cdot)$$ n/a 10624 16
4641.2.mg $$\chi_{4641}(278, \cdot)$$ n/a 10624 16
4641.2.mh $$\chi_{4641}(109, \cdot)$$ n/a 5376 16
4641.2.mk $$\chi_{4641}(479, \cdot)$$ n/a 10624 16
4641.2.ml $$\chi_{4641}(58, \cdot)$$ n/a 5376 16
4641.2.mm $$\chi_{4641}(116, \cdot)$$ n/a 10624 16
4641.2.mo $$\chi_{4641}(40, \cdot)$$ n/a 4608 16
4641.2.mr $$\chi_{4641}(464, \cdot)$$ n/a 10624 16
4641.2.ms $$\chi_{4641}(160, \cdot)$$ n/a 5376 16
4641.2.mu $$\chi_{4641}(29, \cdot)$$ n/a 8064 16
4641.2.mx $$\chi_{4641}(10, \cdot)$$ n/a 5376 16
4641.2.mz $$\chi_{4641}(61, \cdot)$$ n/a 5376 16
4641.2.na $$\chi_{4641}(218, \cdot)$$ n/a 8064 16
4641.2.nc $$\chi_{4641}(139, \cdot)$$ n/a 5376 16
4641.2.nf $$\chi_{4641}(452, \cdot)$$ n/a 10624 16
4641.2.ng $$\chi_{4641}(649, \cdot)$$ n/a 5376 16
4641.2.ni $$\chi_{4641}(326, \cdot)$$ n/a 9216 16
4641.2.nm $$\chi_{4641}(5, \cdot)$$ n/a 10624 16
4641.2.nn $$\chi_{4641}(226, \cdot)$$ n/a 5376 16
4641.2.nq $$\chi_{4641}(80, \cdot)$$ n/a 10624 16
4641.2.nr $$\chi_{4641}(163, \cdot)$$ n/a 5376 16
4641.2.ns $$\chi_{4641}(505, \cdot)$$ n/a 4032 16
4641.2.nt $$\chi_{4641}(20, \cdot)$$ n/a 10624 16

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

Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(4641))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(4641)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(13))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 8}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(21))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(39))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(91))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(119))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(221))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(273))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(357))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(663))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(1547))$$$$^{\oplus 2}$$