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Properties

Label 25410.2
Level 25410
Weight 2
Dimension 3613088
Nonzero newspaces 96
Sturm bound 66908160

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Defining parameters

Level: \( N \) = \( 25410 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 96 \)
Sturm bound: \(66908160\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(25410))\).

Total New Old
Modular forms 16788480 3613088 13175392
Cusp forms 16665601 3613088 13052513
Eisenstein series 122879 0 122879

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(25410))\)

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
25410.2.a \(\chi_{25410}(1, \cdot)\) 25410.2.a.a 1 1
25410.2.a.b 1
25410.2.a.c 1
25410.2.a.d 1
25410.2.a.e 1
25410.2.a.f 1
25410.2.a.g 1
25410.2.a.h 1
25410.2.a.i 1
25410.2.a.j 1
25410.2.a.k 1
25410.2.a.l 1
25410.2.a.m 1
25410.2.a.n 1
25410.2.a.o 1
25410.2.a.p 1
25410.2.a.q 1
25410.2.a.r 1
25410.2.a.s 1
25410.2.a.t 1
25410.2.a.u 1
25410.2.a.v 1
25410.2.a.w 1
25410.2.a.x 1
25410.2.a.y 1
25410.2.a.z 1
25410.2.a.ba 1
25410.2.a.bb 1
25410.2.a.bc 1
25410.2.a.bd 1
25410.2.a.be 1
25410.2.a.bf 1
25410.2.a.bg 1
25410.2.a.bh 1
25410.2.a.bi 1
25410.2.a.bj 1
25410.2.a.bk 1
25410.2.a.bl 1
25410.2.a.bm 1
25410.2.a.bn 1
25410.2.a.bo 1
25410.2.a.bp 1
25410.2.a.bq 1
25410.2.a.br 1
25410.2.a.bs 1
25410.2.a.bt 1
25410.2.a.bu 1
25410.2.a.bv 1
25410.2.a.bw 1
25410.2.a.bx 1
25410.2.a.by 1
25410.2.a.bz 1
25410.2.a.ca 1
25410.2.a.cb 1
25410.2.a.cc 1
25410.2.a.cd 1
25410.2.a.ce 1
25410.2.a.cf 1
25410.2.a.cg 1
25410.2.a.ch 1
25410.2.a.ci 1
25410.2.a.cj 1
25410.2.a.ck 1
25410.2.a.cl 1
25410.2.a.cm 1
25410.2.a.cn 1
25410.2.a.co 1
25410.2.a.cp 1
25410.2.a.cq 1
25410.2.a.cr 1
25410.2.a.cs 1
25410.2.a.ct 1
25410.2.a.cu 1
25410.2.a.cv 1
25410.2.a.cw 1
25410.2.a.cx 1
25410.2.a.cy 1
25410.2.a.cz 2
25410.2.a.da 2
25410.2.a.db 2
25410.2.a.dc 2
25410.2.a.dd 2
25410.2.a.de 2
25410.2.a.df 2
25410.2.a.dg 2
25410.2.a.dh 2
25410.2.a.di 2
25410.2.a.dj 2
25410.2.a.dk 2
25410.2.a.dl 2
25410.2.a.dm 2
25410.2.a.dn 2
25410.2.a.do 2
25410.2.a.dp 2
25410.2.a.dq 2
25410.2.a.dr 2
25410.2.a.ds 2
25410.2.a.dt 2
25410.2.a.du 2
25410.2.a.dv 2
25410.2.a.dw 2
25410.2.a.dx 2
25410.2.a.dy 2
25410.2.a.dz 2
25410.2.a.ea 2
25410.2.a.eb 2
25410.2.a.ec 2
25410.2.a.ed 2
25410.2.a.ee 2
25410.2.a.ef 2
25410.2.a.eg 2
25410.2.a.eh 2
25410.2.a.ei 2
25410.2.a.ej 2
25410.2.a.ek 3
25410.2.a.el 3
25410.2.a.em 3
25410.2.a.en 3
25410.2.a.eo 3
25410.2.a.ep 3
25410.2.a.eq 3
25410.2.a.er 4
25410.2.a.es 4
25410.2.a.et 4
25410.2.a.eu 4
25410.2.a.ev 4
25410.2.a.ew 4
25410.2.a.ex 4
25410.2.a.ey 4
25410.2.a.ez 4
25410.2.a.fa 4
25410.2.a.fb 4
25410.2.a.fc 4
25410.2.a.fd 4
25410.2.a.fe 4
25410.2.a.ff 4
25410.2.a.fg 4
25410.2.a.fh 4
25410.2.a.fi 4
25410.2.a.fj 4
25410.2.a.fk 4
25410.2.a.fl 4
25410.2.a.fm 4
25410.2.a.fn 4
25410.2.a.fo 4
25410.2.a.fp 6
25410.2.a.fq 6
25410.2.a.fr 6
25410.2.a.fs 6
25410.2.a.ft 6
25410.2.a.fu 6
25410.2.a.fv 6
25410.2.a.fw 6
25410.2.a.fx 6
25410.2.a.fy 6
25410.2.a.fz 6
25410.2.a.ga 6
25410.2.a.gb 6
25410.2.a.gc 6
25410.2.a.gd 6
25410.2.a.ge 6
25410.2.a.gf 6
25410.2.a.gg 6
25410.2.a.gh 6
25410.2.a.gi 6
25410.2.a.gj 8
25410.2.a.gk 8
25410.2.a.gl 8
25410.2.a.gm 8
25410.2.a.gn 8
25410.2.a.go 8
25410.2.d \(\chi_{25410}(16939, \cdot)\) n/a 864 1
25410.2.e \(\chi_{25410}(20329, \cdot)\) n/a 652 1
25410.2.f \(\chi_{25410}(19361, \cdot)\) n/a 1160 1
25410.2.g \(\chi_{25410}(19601, \cdot)\) n/a 864 1
25410.2.j \(\chi_{25410}(14279, \cdot)\) n/a 1744 1
25410.2.k \(\chi_{25410}(14519, \cdot)\) n/a 1296 1
25410.2.p \(\chi_{25410}(22021, \cdot)\) n/a 576 1
25410.2.q \(\chi_{25410}(7261, \cdot)\) n/a 1160 2
25410.2.r \(\chi_{25410}(10163, \cdot)\) n/a 3456 2
25410.2.u \(\chi_{25410}(13553, \cdot)\) n/a 2616 2
25410.2.v \(\chi_{25410}(727, \cdot)\) n/a 1744 2
25410.2.y \(\chi_{25410}(967, \cdot)\) n/a 1296 2
25410.2.z \(\chi_{25410}(6301, \cdot)\) n/a 1728 4
25410.2.bc \(\chi_{25410}(12101, \cdot)\) n/a 2328 2
25410.2.bd \(\chi_{25410}(1451, \cdot)\) n/a 2304 2
25410.2.be \(\chi_{25410}(9679, \cdot)\) n/a 1728 2
25410.2.bf \(\chi_{25410}(2179, \cdot)\) n/a 1744 2
25410.2.bi \(\chi_{25410}(241, \cdot)\) n/a 1152 2
25410.2.bn \(\chi_{25410}(7019, \cdot)\) n/a 3488 2
25410.2.bo \(\chi_{25410}(10889, \cdot)\) n/a 3456 2
25410.2.bp \(\chi_{25410}(7741, \cdot)\) n/a 2304 4
25410.2.bu \(\chi_{25410}(239, \cdot)\) n/a 5184 4
25410.2.bv \(\chi_{25410}(1049, \cdot)\) n/a 6912 4
25410.2.by \(\chi_{25410}(5321, \cdot)\) n/a 3456 4
25410.2.bz \(\chi_{25410}(251, \cdot)\) n/a 4608 4
25410.2.ca \(\chi_{25410}(1219, \cdot)\) n/a 2592 4
25410.2.cb \(\chi_{25410}(2659, \cdot)\) n/a 3456 4
25410.2.ce \(\chi_{25410}(2311, \cdot)\) n/a 5280 10
25410.2.cg \(\chi_{25410}(4357, \cdot)\) n/a 3488 4
25410.2.ch \(\chi_{25410}(8227, \cdot)\) n/a 3456 4
25410.2.ck \(\chi_{25410}(2903, \cdot)\) n/a 6912 4
25410.2.cl \(\chi_{25410}(5567, \cdot)\) n/a 6976 4
25410.2.cn \(\chi_{25410}(2671, \cdot)\) n/a 4608 8
25410.2.co \(\chi_{25410}(1933, \cdot)\) n/a 5184 8
25410.2.cr \(\chi_{25410}(2743, \cdot)\) n/a 6912 8
25410.2.cs \(\chi_{25410}(323, \cdot)\) n/a 10368 8
25410.2.cv \(\chi_{25410}(2393, \cdot)\) n/a 13824 8
25410.2.cw \(\chi_{25410}(1231, \cdot)\) n/a 7040 10
25410.2.db \(\chi_{25410}(659, \cdot)\) n/a 15840 10
25410.2.dc \(\chi_{25410}(419, \cdot)\) n/a 21120 10
25410.2.df \(\chi_{25410}(1121, \cdot)\) n/a 10560 10
25410.2.dg \(\chi_{25410}(881, \cdot)\) n/a 14080 10
25410.2.dh \(\chi_{25410}(1849, \cdot)\) n/a 7920 10
25410.2.di \(\chi_{25410}(769, \cdot)\) n/a 10560 10
25410.2.dl \(\chi_{25410}(3119, \cdot)\) n/a 13824 8
25410.2.dm \(\chi_{25410}(269, \cdot)\) n/a 13824 8
25410.2.dr \(\chi_{25410}(481, \cdot)\) n/a 4608 8
25410.2.du \(\chi_{25410}(3469, \cdot)\) n/a 6912 8
25410.2.dv \(\chi_{25410}(1909, \cdot)\) n/a 6912 8
25410.2.dw \(\chi_{25410}(1691, \cdot)\) n/a 9216 8
25410.2.dx \(\chi_{25410}(971, \cdot)\) n/a 9216 8
25410.2.ea \(\chi_{25410}(331, \cdot)\) n/a 14080 20
25410.2.eb \(\chi_{25410}(43, \cdot)\) n/a 15840 20
25410.2.ee \(\chi_{25410}(2113, \cdot)\) n/a 21120 20
25410.2.ef \(\chi_{25410}(617, \cdot)\) n/a 31680 20
25410.2.ei \(\chi_{25410}(923, \cdot)\) n/a 42240 20
25410.2.ej \(\chi_{25410}(421, \cdot)\) n/a 21120 40
25410.2.el \(\chi_{25410}(977, \cdot)\) n/a 27648 16
25410.2.em \(\chi_{25410}(887, \cdot)\) n/a 27648 16
25410.2.ep \(\chi_{25410}(403, \cdot)\) n/a 13824 16
25410.2.eq \(\chi_{25410}(493, \cdot)\) n/a 13824 16
25410.2.es \(\chi_{25410}(989, \cdot)\) n/a 42240 20
25410.2.et \(\chi_{25410}(89, \cdot)\) n/a 42240 20
25410.2.ey \(\chi_{25410}(901, \cdot)\) n/a 14080 20
25410.2.fb \(\chi_{25410}(529, \cdot)\) n/a 21120 20
25410.2.fc \(\chi_{25410}(439, \cdot)\) n/a 21120 20
25410.2.fd \(\chi_{25410}(2111, \cdot)\) n/a 28160 20
25410.2.fe \(\chi_{25410}(551, \cdot)\) n/a 28160 20
25410.2.fj \(\chi_{25410}(139, \cdot)\) n/a 42240 40
25410.2.fk \(\chi_{25410}(169, \cdot)\) n/a 31680 40
25410.2.fl \(\chi_{25410}(1301, \cdot)\) n/a 56320 40
25410.2.fm \(\chi_{25410}(281, \cdot)\) n/a 42240 40
25410.2.fp \(\chi_{25410}(839, \cdot)\) n/a 84480 40
25410.2.fq \(\chi_{25410}(29, \cdot)\) n/a 63360 40
25410.2.fv \(\chi_{25410}(391, \cdot)\) n/a 28160 40
25410.2.fx \(\chi_{25410}(23, \cdot)\) n/a 84480 40
25410.2.fy \(\chi_{25410}(593, \cdot)\) n/a 84480 40
25410.2.gb \(\chi_{25410}(373, \cdot)\) n/a 42240 40
25410.2.gc \(\chi_{25410}(397, \cdot)\) n/a 42240 40
25410.2.ge \(\chi_{25410}(361, \cdot)\) n/a 56320 80
25410.2.gf \(\chi_{25410}(83, \cdot)\) n/a 168960 80
25410.2.gi \(\chi_{25410}(113, \cdot)\) n/a 126720 80
25410.2.gj \(\chi_{25410}(97, \cdot)\) n/a 84480 80
25410.2.gm \(\chi_{25410}(127, \cdot)\) n/a 63360 80
25410.2.gp \(\chi_{25410}(311, \cdot)\) n/a 112640 80
25410.2.gq \(\chi_{25410}(431, \cdot)\) n/a 112640 80
25410.2.gr \(\chi_{25410}(19, \cdot)\) n/a 84480 80
25410.2.gs \(\chi_{25410}(289, \cdot)\) n/a 84480 80
25410.2.gv \(\chi_{25410}(61, \cdot)\) n/a 56320 80
25410.2.ha \(\chi_{25410}(59, \cdot)\) n/a 168960 80
25410.2.hb \(\chi_{25410}(149, \cdot)\) n/a 168960 80
25410.2.hd \(\chi_{25410}(103, \cdot)\) n/a 168960 160
25410.2.he \(\chi_{25410}(193, \cdot)\) n/a 168960 160
25410.2.hh \(\chi_{25410}(17, \cdot)\) n/a 337920 160
25410.2.hi \(\chi_{25410}(53, \cdot)\) n/a 337920 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(25410))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(25410)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 48}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 32}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(21))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(33))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(35))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(42))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(66))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(70))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(77))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(105))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(154))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(165))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(210))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(231))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(330))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(363))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(385))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(462))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(726))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(770))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(847))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1155))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1694))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1815))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2310))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2541))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3630))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4235))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5082))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8470))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12705))\)\(^{\oplus 2}\)