↑

Properties

Label 15730.2
Level 15730
Weight 2
Dimension 2173096
Nonzero newspaces 80
Sturm bound 29272320

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 15730 = 2 \cdot 5 \cdot 11^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 80 \)
Sturm bound: \(29272320\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(15730))\).

Total New Old
Modular forms 7348800 2173096 5175704
Cusp forms 7287361 2173096 5114265
Eisenstein series 61439 0 61439

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(15730))\)

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
15730.2.a \(\chi_{15730}(1, \cdot)\) 15730.2.a.a 1 1
15730.2.a.b 1
15730.2.a.c 1
15730.2.a.d 1
15730.2.a.e 1
15730.2.a.f 1
15730.2.a.g 1
15730.2.a.h 1
15730.2.a.i 1
15730.2.a.j 1
15730.2.a.k 1
15730.2.a.l 1
15730.2.a.m 1
15730.2.a.n 1
15730.2.a.o 1
15730.2.a.p 1
15730.2.a.q 1
15730.2.a.r 1
15730.2.a.s 1
15730.2.a.t 1
15730.2.a.u 1
15730.2.a.v 1
15730.2.a.w 1
15730.2.a.x 1
15730.2.a.y 1
15730.2.a.z 1
15730.2.a.ba 1
15730.2.a.bb 1
15730.2.a.bc 1
15730.2.a.bd 1
15730.2.a.be 2
15730.2.a.bf 2
15730.2.a.bg 2
15730.2.a.bh 2
15730.2.a.bi 2
15730.2.a.bj 2
15730.2.a.bk 2
15730.2.a.bl 2
15730.2.a.bm 2
15730.2.a.bn 2
15730.2.a.bo 2
15730.2.a.bp 3
15730.2.a.bq 3
15730.2.a.br 3
15730.2.a.bs 3
15730.2.a.bt 3
15730.2.a.bu 3
15730.2.a.bv 3
15730.2.a.bw 3
15730.2.a.bx 3
15730.2.a.by 3
15730.2.a.bz 3
15730.2.a.ca 3
15730.2.a.cb 4
15730.2.a.cc 4
15730.2.a.cd 4
15730.2.a.ce 4
15730.2.a.cf 4
15730.2.a.cg 4
15730.2.a.ch 4
15730.2.a.ci 4
15730.2.a.cj 5
15730.2.a.ck 5
15730.2.a.cl 5
15730.2.a.cm 5
15730.2.a.cn 5
15730.2.a.co 5
15730.2.a.cp 5
15730.2.a.cq 5
15730.2.a.cr 6
15730.2.a.cs 6
15730.2.a.ct 6
15730.2.a.cu 6
15730.2.a.cv 6
15730.2.a.cw 6
15730.2.a.cx 6
15730.2.a.cy 6
15730.2.a.cz 8
15730.2.a.da 8
15730.2.a.db 8
15730.2.a.dc 8
15730.2.a.dd 10
15730.2.a.de 10
15730.2.a.df 10
15730.2.a.dg 10
15730.2.a.dh 10
15730.2.a.di 10
15730.2.a.dj 12
15730.2.a.dk 12
15730.2.a.dl 12
15730.2.a.dm 12
15730.2.a.dn 14
15730.2.a.do 14
15730.2.a.dp 14
15730.2.a.dq 14
15730.2.a.dr 16
15730.2.a.ds 16
15730.2.b \(\chi_{15730}(9439, \cdot)\) n/a 654 1
15730.2.d \(\chi_{15730}(7019, \cdot)\) n/a 764 1
15730.2.g \(\chi_{15730}(13311, \cdot)\) n/a 506 1
15730.2.i \(\chi_{15730}(2421, \cdot)\) n/a 1020 2
15730.2.j \(\chi_{15730}(7259, \cdot)\) n/a 1512 2
15730.2.l \(\chi_{15730}(7987, \cdot)\) n/a 1526 2
15730.2.o \(\chi_{15730}(9437, \cdot)\) n/a 1512 2
15730.2.q \(\chi_{15730}(11857, \cdot)\) n/a 1296 2
15730.2.r \(\chi_{15730}(11133, \cdot)\) n/a 1526 2
15730.2.u \(\chi_{15730}(1451, \cdot)\) n/a 1008 2
15730.2.v \(\chi_{15730}(7021, \cdot)\) n/a 1728 4
15730.2.x \(\chi_{15730}(3631, \cdot)\) n/a 1020 2
15730.2.ba \(\chi_{15730}(4599, \cdot)\) n/a 1528 2
15730.2.bc \(\chi_{15730}(3389, \cdot)\) n/a 1524 2
15730.2.be \(\chi_{15730}(4601, \cdot)\) n/a 2016 4
15730.2.bh \(\chi_{15730}(3639, \cdot)\) n/a 3024 4
15730.2.bj \(\chi_{15730}(729, \cdot)\) n/a 2592 4
15730.2.bk \(\chi_{15730}(1431, \cdot)\) n/a 5280 10
15730.2.bl \(\chi_{15730}(241, \cdot)\) n/a 2016 4
15730.2.bo \(\chi_{15730}(7503, \cdot)\) n/a 3052 4
15730.2.bp \(\chi_{15730}(1693, \cdot)\) n/a 3024 4
15730.2.br \(\chi_{15730}(2903, \cdot)\) n/a 3024 4
15730.2.bu \(\chi_{15730}(2663, \cdot)\) n/a 3052 4
15730.2.bw \(\chi_{15730}(3629, \cdot)\) n/a 3024 4
15730.2.bx \(\chi_{15730}(81, \cdot)\) n/a 4032 8
15730.2.by \(\chi_{15730}(161, \cdot)\) n/a 4032 8
15730.2.cb \(\chi_{15730}(2423, \cdot)\) n/a 6048 8
15730.2.cc \(\chi_{15730}(1613, \cdot)\) n/a 5184 8
15730.2.ce \(\chi_{15730}(233, \cdot)\) n/a 6048 8
15730.2.ch \(\chi_{15730}(4607, \cdot)\) n/a 6048 8
15730.2.cj \(\chi_{15730}(239, \cdot)\) n/a 6048 8
15730.2.cl \(\chi_{15730}(1299, \cdot)\) n/a 9240 10
15730.2.cn \(\chi_{15730}(859, \cdot)\) n/a 7920 10
15730.2.cp \(\chi_{15730}(441, \cdot)\) n/a 6160 10
15730.2.cr \(\chi_{15730}(9, \cdot)\) n/a 6048 8
15730.2.ct \(\chi_{15730}(1219, \cdot)\) n/a 6048 8
15730.2.cw \(\chi_{15730}(251, \cdot)\) n/a 4032 8
15730.2.cy \(\chi_{15730}(991, \cdot)\) n/a 12320 20
15730.2.da \(\chi_{15730}(109, \cdot)\) n/a 18480 20
15730.2.dc \(\chi_{15730}(177, \cdot)\) n/a 18480 20
15730.2.dd \(\chi_{15730}(417, \cdot)\) n/a 15840 20
15730.2.df \(\chi_{15730}(857, \cdot)\) n/a 18480 20
15730.2.di \(\chi_{15730}(463, \cdot)\) n/a 18480 20
15730.2.dj \(\chi_{15730}(21, \cdot)\) n/a 12320 20
15730.2.dl \(\chi_{15730}(521, \cdot)\) n/a 21120 40
15730.2.dm \(\chi_{15730}(1129, \cdot)\) n/a 12096 16
15730.2.do \(\chi_{15730}(323, \cdot)\) n/a 12096 16
15730.2.dr \(\chi_{15730}(2097, \cdot)\) n/a 12096 16
15730.2.dt \(\chi_{15730}(887, \cdot)\) n/a 12096 16
15730.2.du \(\chi_{15730}(1697, \cdot)\) n/a 12096 16
15730.2.dx \(\chi_{15730}(1371, \cdot)\) n/a 8064 16
15730.2.dz \(\chi_{15730}(771, \cdot)\) n/a 12320 20
15730.2.eb \(\chi_{15730}(419, \cdot)\) n/a 18480 20
15730.2.ed \(\chi_{15730}(199, \cdot)\) n/a 18480 20
15730.2.eg \(\chi_{15730}(181, \cdot)\) n/a 24640 40
15730.2.ei \(\chi_{15730}(339, \cdot)\) n/a 31680 40
15730.2.ek \(\chi_{15730}(389, \cdot)\) n/a 36960 40
15730.2.en \(\chi_{15730}(461, \cdot)\) n/a 24640 40
15730.2.eo \(\chi_{15730}(67, \cdot)\) n/a 36960 40
15730.2.er \(\chi_{15730}(43, \cdot)\) n/a 36960 40
15730.2.et \(\chi_{15730}(87, \cdot)\) n/a 36960 40
15730.2.eu \(\chi_{15730}(353, \cdot)\) n/a 36960 40
15730.2.ew \(\chi_{15730}(219, \cdot)\) n/a 36960 40
15730.2.ey \(\chi_{15730}(191, \cdot)\) n/a 49280 80
15730.2.fa \(\chi_{15730}(151, \cdot)\) n/a 49280 80
15730.2.fb \(\chi_{15730}(203, \cdot)\) n/a 73920 80
15730.2.fe \(\chi_{15730}(337, \cdot)\) n/a 73920 80
15730.2.fg \(\chi_{15730}(183, \cdot)\) n/a 63360 80
15730.2.fh \(\chi_{15730}(47, \cdot)\) n/a 73920 80
15730.2.fj \(\chi_{15730}(359, \cdot)\) n/a 73920 80
15730.2.fm \(\chi_{15730}(49, \cdot)\) n/a 73920 80
15730.2.fo \(\chi_{15730}(159, \cdot)\) n/a 73920 80
15730.2.fq \(\chi_{15730}(361, \cdot)\) n/a 49280 80
15730.2.ft \(\chi_{15730}(19, \cdot)\) n/a 147840 160
15730.2.fv \(\chi_{15730}(37, \cdot)\) n/a 147840 160
15730.2.fw \(\chi_{15730}(107, \cdot)\) n/a 147840 160
15730.2.fy \(\chi_{15730}(17, \cdot)\) n/a 147840 160
15730.2.gb \(\chi_{15730}(97, \cdot)\) n/a 147840 160
15730.2.gc \(\chi_{15730}(41, \cdot)\) n/a 98560 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(15730))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(15730)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(11))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(22))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(55))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(110))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(121))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(143))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(242))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(286))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(605))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(715))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1210))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1430))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1573))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3146))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7865))\)\(^{\oplus 2}\)