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Properties

Label 10944.2
Level 10944
Weight 2
Dimension 1465866
Nonzero newspaces 128
Sturm bound 13271040

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Defining parameters

Level: \( N \) = \( 10944 = 2^{6} \cdot 3^{2} \cdot 19 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 128 \)
Sturm bound: \(13271040\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(10944))\).

Total New Old
Modular forms 3338496 1472598 1865898
Cusp forms 3297025 1465866 1831159
Eisenstein series 41471 6732 34739

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(10944))\)

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
10944.2.a \(\chi_{10944}(1, \cdot)\) 10944.2.a.a 1 1
10944.2.a.b 1
10944.2.a.c 1
10944.2.a.d 1
10944.2.a.e 1
10944.2.a.f 1
10944.2.a.g 1
10944.2.a.h 1
10944.2.a.i 1
10944.2.a.j 1
10944.2.a.k 1
10944.2.a.l 1
10944.2.a.m 1
10944.2.a.n 1
10944.2.a.o 1
10944.2.a.p 1
10944.2.a.q 1
10944.2.a.r 1
10944.2.a.s 1
10944.2.a.t 1
10944.2.a.u 1
10944.2.a.v 1
10944.2.a.w 1
10944.2.a.x 1
10944.2.a.y 1
10944.2.a.z 1
10944.2.a.ba 1
10944.2.a.bb 1
10944.2.a.bc 1
10944.2.a.bd 1
10944.2.a.be 1
10944.2.a.bf 1
10944.2.a.bg 1
10944.2.a.bh 1
10944.2.a.bi 1
10944.2.a.bj 1
10944.2.a.bk 1
10944.2.a.bl 1
10944.2.a.bm 1
10944.2.a.bn 1
10944.2.a.bo 1
10944.2.a.bp 1
10944.2.a.bq 1
10944.2.a.br 1
10944.2.a.bs 1
10944.2.a.bt 1
10944.2.a.bu 1
10944.2.a.bv 1
10944.2.a.bw 1
10944.2.a.bx 1
10944.2.a.by 1
10944.2.a.bz 1
10944.2.a.ca 1
10944.2.a.cb 1
10944.2.a.cc 1
10944.2.a.cd 1
10944.2.a.ce 1
10944.2.a.cf 1
10944.2.a.cg 1
10944.2.a.ch 1
10944.2.a.ci 1
10944.2.a.cj 1
10944.2.a.ck 1
10944.2.a.cl 1
10944.2.a.cm 1
10944.2.a.cn 1
10944.2.a.co 1
10944.2.a.cp 1
10944.2.a.cq 1
10944.2.a.cr 1
10944.2.a.cs 2
10944.2.a.ct 2
10944.2.a.cu 2
10944.2.a.cv 2
10944.2.a.cw 2
10944.2.a.cx 2
10944.2.a.cy 2
10944.2.a.cz 2
10944.2.a.da 2
10944.2.a.db 2
10944.2.a.dc 2
10944.2.a.dd 2
10944.2.a.de 2
10944.2.a.df 2
10944.2.a.dg 2
10944.2.a.dh 2
10944.2.a.di 2
10944.2.a.dj 2
10944.2.a.dk 2
10944.2.a.dl 2
10944.2.a.dm 2
10944.2.a.dn 2
10944.2.a.do 2
10944.2.a.dp 2
10944.2.a.dq 3
10944.2.a.dr 3
10944.2.a.ds 3
10944.2.a.dt 3
10944.2.a.du 3
10944.2.a.dv 3
10944.2.a.dw 3
10944.2.a.dx 3
10944.2.a.dy 3
10944.2.a.dz 3
10944.2.a.ea 4
10944.2.a.eb 4
10944.2.a.ec 4
10944.2.a.ed 4
10944.2.a.ee 4
10944.2.a.ef 4
10944.2.a.eg 4
10944.2.a.eh 4
10944.2.d \(\chi_{10944}(7487, \cdot)\) n/a 144 1
10944.2.e \(\chi_{10944}(7903, \cdot)\) n/a 200 1
10944.2.f \(\chi_{10944}(1025, \cdot)\) n/a 160 1
10944.2.g \(\chi_{10944}(5473, \cdot)\) n/a 180 1
10944.2.j \(\chi_{10944}(2015, \cdot)\) n/a 144 1
10944.2.k \(\chi_{10944}(2431, \cdot)\) n/a 198 1
10944.2.p \(\chi_{10944}(6497, \cdot)\) n/a 160 1
10944.2.q \(\chi_{10944}(3649, \cdot)\) n/a 864 2
10944.2.r \(\chi_{10944}(7873, \cdot)\) n/a 952 2
10944.2.s \(\chi_{10944}(577, \cdot)\) n/a 396 2
10944.2.t \(\chi_{10944}(961, \cdot)\) n/a 952 2
10944.2.u \(\chi_{10944}(3761, \cdot)\) n/a 320 2
10944.2.x \(\chi_{10944}(2737, \cdot)\) n/a 360 2
10944.2.y \(\chi_{10944}(4751, \cdot)\) n/a 288 2
10944.2.bb \(\chi_{10944}(5167, \cdot)\) n/a 396 2
10944.2.be \(\chi_{10944}(6433, \cdot)\) n/a 960 2
10944.2.bf \(\chi_{10944}(65, \cdot)\) n/a 952 2
10944.2.bg \(\chi_{10944}(31, \cdot)\) n/a 960 2
10944.2.bh \(\chi_{10944}(4415, \cdot)\) n/a 952 2
10944.2.bm \(\chi_{10944}(1855, \cdot)\) n/a 396 2
10944.2.bn \(\chi_{10944}(2591, \cdot)\) n/a 320 2
10944.2.bq \(\chi_{10944}(2849, \cdot)\) n/a 960 2
10944.2.bt \(\chi_{10944}(9185, \cdot)\) n/a 960 2
10944.2.bu \(\chi_{10944}(1471, \cdot)\) n/a 952 2
10944.2.bv \(\chi_{10944}(2975, \cdot)\) n/a 960 2
10944.2.by \(\chi_{10944}(5663, \cdot)\) n/a 864 2
10944.2.bz \(\chi_{10944}(6079, \cdot)\) n/a 952 2
10944.2.cc \(\chi_{10944}(1889, \cdot)\) n/a 320 2
10944.2.cf \(\chi_{10944}(3295, \cdot)\) n/a 400 2
10944.2.cg \(\chi_{10944}(1151, \cdot)\) n/a 320 2
10944.2.cj \(\chi_{10944}(2401, \cdot)\) n/a 960 2
10944.2.ck \(\chi_{10944}(3713, \cdot)\) n/a 952 2
10944.2.cn \(\chi_{10944}(4673, \cdot)\) n/a 952 2
10944.2.co \(\chi_{10944}(1825, \cdot)\) n/a 864 2
10944.2.ct \(\chi_{10944}(191, \cdot)\) n/a 864 2
10944.2.cu \(\chi_{10944}(607, \cdot)\) n/a 960 2
10944.2.cx \(\chi_{10944}(3679, \cdot)\) n/a 960 2
10944.2.cy \(\chi_{10944}(767, \cdot)\) n/a 952 2
10944.2.db \(\chi_{10944}(6049, \cdot)\) n/a 400 2
10944.2.dc \(\chi_{10944}(449, \cdot)\) n/a 320 2
10944.2.dd \(\chi_{10944}(2273, \cdot)\) n/a 960 2
10944.2.di \(\chi_{10944}(5119, \cdot)\) n/a 952 2
10944.2.dj \(\chi_{10944}(9887, \cdot)\) n/a 960 2
10944.2.ds \(\chi_{10944}(2305, \cdot)\) n/a 1188 6
10944.2.dt \(\chi_{10944}(2113, \cdot)\) n/a 2856 6
10944.2.du \(\chi_{10944}(385, \cdot)\) n/a 2856 6
10944.2.dw \(\chi_{10944}(1873, \cdot)\) n/a 792 4
10944.2.dx \(\chi_{10944}(3185, \cdot)\) n/a 640 4
10944.2.ea \(\chi_{10944}(1103, \cdot)\) n/a 1728 4
10944.2.eb \(\chi_{10944}(2383, \cdot)\) n/a 1904 4
10944.2.ed \(\chi_{10944}(943, \cdot)\) n/a 1904 4
10944.2.eg \(\chi_{10944}(239, \cdot)\) n/a 1904 4
10944.2.ei \(\chi_{10944}(1679, \cdot)\) n/a 1904 4
10944.2.ej \(\chi_{10944}(1519, \cdot)\) n/a 1904 4
10944.2.em \(\chi_{10944}(113, \cdot)\) n/a 1904 4
10944.2.en \(\chi_{10944}(49, \cdot)\) n/a 1904 4
10944.2.ep \(\chi_{10944}(1489, \cdot)\) n/a 1904 4
10944.2.es \(\chi_{10944}(2801, \cdot)\) n/a 1904 4
10944.2.eu \(\chi_{10944}(977, \cdot)\) n/a 1904 4
10944.2.ev \(\chi_{10944}(913, \cdot)\) n/a 1728 4
10944.2.ey \(\chi_{10944}(559, \cdot)\) n/a 792 4
10944.2.ez \(\chi_{10944}(3887, \cdot)\) n/a 640 4
10944.2.fc \(\chi_{10944}(379, \cdot)\) n/a 6384 8
10944.2.fd \(\chi_{10944}(685, \cdot)\) n/a 5760 8
10944.2.ff \(\chi_{10944}(1331, \cdot)\) n/a 4608 8
10944.2.fi \(\chi_{10944}(341, \cdot)\) n/a 5120 8
10944.2.fk \(\chi_{10944}(223, \cdot)\) n/a 2880 6
10944.2.fm \(\chi_{10944}(959, \cdot)\) n/a 2856 6
10944.2.fn \(\chi_{10944}(319, \cdot)\) n/a 2856 6
10944.2.fp \(\chi_{10944}(671, \cdot)\) n/a 2880 6
10944.2.fr \(\chi_{10944}(1409, \cdot)\) n/a 2856 6
10944.2.ft \(\chi_{10944}(2209, \cdot)\) n/a 2880 6
10944.2.fx \(\chi_{10944}(737, \cdot)\) n/a 960 6
10944.2.fy \(\chi_{10944}(289, \cdot)\) n/a 1200 6
10944.2.ga \(\chi_{10944}(3905, \cdot)\) n/a 960 6
10944.2.gd \(\chi_{10944}(2081, \cdot)\) n/a 2880 6
10944.2.gf \(\chi_{10944}(479, \cdot)\) n/a 2880 6
10944.2.gh \(\chi_{10944}(895, \cdot)\) n/a 2856 6
10944.2.gk \(\chi_{10944}(991, \cdot)\) n/a 1200 6
10944.2.gm \(\chi_{10944}(575, \cdot)\) n/a 960 6
10944.2.gn \(\chi_{10944}(127, \cdot)\) n/a 1188 6
10944.2.gp \(\chi_{10944}(4319, \cdot)\) n/a 960 6
10944.2.gs \(\chi_{10944}(2495, \cdot)\) n/a 2856 6
10944.2.gu \(\chi_{10944}(1951, \cdot)\) n/a 2880 6
10944.2.gx \(\chi_{10944}(545, \cdot)\) n/a 2880 6
10944.2.gy \(\chi_{10944}(481, \cdot)\) n/a 2880 6
10944.2.ha \(\chi_{10944}(257, \cdot)\) n/a 2856 6
10944.2.ii \(\chi_{10944}(529, \cdot)\) n/a 5712 12
10944.2.ik \(\chi_{10944}(497, \cdot)\) n/a 5712 12
10944.2.im \(\chi_{10944}(47, \cdot)\) n/a 5712 12
10944.2.ip \(\chi_{10944}(1135, \cdot)\) n/a 2376 12
10944.2.ir \(\chi_{10944}(719, \cdot)\) n/a 1920 12
10944.2.is \(\chi_{10944}(1231, \cdot)\) n/a 5712 12
10944.2.iv \(\chi_{10944}(401, \cdot)\) n/a 5712 12
10944.2.iw \(\chi_{10944}(1297, \cdot)\) n/a 2376 12
10944.2.iy \(\chi_{10944}(1169, \cdot)\) n/a 1920 12
10944.2.jb \(\chi_{10944}(625, \cdot)\) n/a 5712 12
10944.2.jd \(\chi_{10944}(79, \cdot)\) n/a 5712 12
10944.2.jf \(\chi_{10944}(1391, \cdot)\) n/a 5712 12
10944.2.jg \(\chi_{10944}(1171, \cdot)\) n/a 12768 16
10944.2.jj \(\chi_{10944}(1189, \cdot)\) n/a 12768 16
10944.2.jl \(\chi_{10944}(797, \cdot)\) n/a 30656 16
10944.2.jm \(\chi_{10944}(221, \cdot)\) n/a 30656 16
10944.2.jp \(\chi_{10944}(293, \cdot)\) n/a 30656 16
10944.2.jq \(\chi_{10944}(83, \cdot)\) n/a 30656 16
10944.2.jt \(\chi_{10944}(419, \cdot)\) n/a 27648 16
10944.2.ju \(\chi_{10944}(11, \cdot)\) n/a 30656 16
10944.2.jw \(\chi_{10944}(349, \cdot)\) n/a 30656 16
10944.2.jz \(\chi_{10944}(277, \cdot)\) n/a 30656 16
10944.2.ka \(\chi_{10944}(229, \cdot)\) n/a 27648 16
10944.2.kd \(\chi_{10944}(331, \cdot)\) n/a 30656 16
10944.2.ke \(\chi_{10944}(835, \cdot)\) n/a 30656 16
10944.2.kh \(\chi_{10944}(259, \cdot)\) n/a 30656 16
10944.2.kj \(\chi_{10944}(467, \cdot)\) n/a 10240 16
10944.2.kk \(\chi_{10944}(1133, \cdot)\) n/a 10240 16
10944.2.lk \(\chi_{10944}(211, \cdot)\) n/a 91968 48
10944.2.lm \(\chi_{10944}(61, \cdot)\) n/a 91968 48
10944.2.lo \(\chi_{10944}(53, \cdot)\) n/a 30720 48
10944.2.lq \(\chi_{10944}(173, \cdot)\) n/a 91968 48
10944.2.ls \(\chi_{10944}(275, \cdot)\) n/a 91968 48
10944.2.lu \(\chi_{10944}(35, \cdot)\) n/a 30720 48
10944.2.lx \(\chi_{10944}(85, \cdot)\) n/a 91968 48
10944.2.lz \(\chi_{10944}(253, \cdot)\) n/a 38304 48
10944.2.mb \(\chi_{10944}(91, \cdot)\) n/a 38304 48
10944.2.md \(\chi_{10944}(67, \cdot)\) n/a 91968 48
10944.2.mf \(\chi_{10944}(131, \cdot)\) n/a 91968 48
10944.2.mh \(\chi_{10944}(29, \cdot)\) n/a 91968 48

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(10944))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(10944)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 42}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 30}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(19))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(24))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(36))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(38))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(48))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(57))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(72))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(76))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(96))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(114))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(144))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(152))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(171))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(192))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(228))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(288))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(304))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(342))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(456))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(576))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(608))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(684))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(912))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1216))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1368))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1824))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2736))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3648))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5472))\)\(^{\oplus 2}\)