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Properties

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

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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 available 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

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