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Properties

Label 5850.2
Level 5850
Weight 2
Dimension 218021
Nonzero newspaces 100
Sturm bound 3628800

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Defining parameters

Level: \( N \) = \( 5850 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 13 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 100 \)
Sturm bound: \(3628800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(5850))\).

Total New Old
Modular forms 917952 218021 699931
Cusp forms 896449 218021 678428
Eisenstein series 21503 0 21503

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(5850))\)

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
5850.2.a \(\chi_{5850}(1, \cdot)\) 5850.2.a.a 1 1
5850.2.a.b 1
5850.2.a.c 1
5850.2.a.d 1
5850.2.a.e 1
5850.2.a.f 1
5850.2.a.g 1
5850.2.a.h 1
5850.2.a.i 1
5850.2.a.j 1
5850.2.a.k 1
5850.2.a.l 1
5850.2.a.m 1
5850.2.a.n 1
5850.2.a.o 1
5850.2.a.p 1
5850.2.a.q 1
5850.2.a.r 1
5850.2.a.s 1
5850.2.a.t 1
5850.2.a.u 1
5850.2.a.v 1
5850.2.a.w 1
5850.2.a.x 1
5850.2.a.y 1
5850.2.a.z 1
5850.2.a.ba 1
5850.2.a.bb 1
5850.2.a.bc 1
5850.2.a.bd 1
5850.2.a.be 1
5850.2.a.bf 1
5850.2.a.bg 1
5850.2.a.bh 1
5850.2.a.bi 1
5850.2.a.bj 1
5850.2.a.bk 1
5850.2.a.bl 1
5850.2.a.bm 1
5850.2.a.bn 1
5850.2.a.bo 1
5850.2.a.bp 1
5850.2.a.bq 1
5850.2.a.br 1
5850.2.a.bs 1
5850.2.a.bt 1
5850.2.a.bu 1
5850.2.a.bv 1
5850.2.a.bw 1
5850.2.a.bx 1
5850.2.a.by 1
5850.2.a.bz 1
5850.2.a.ca 1
5850.2.a.cb 1
5850.2.a.cc 1
5850.2.a.cd 2
5850.2.a.ce 2
5850.2.a.cf 2
5850.2.a.cg 2
5850.2.a.ch 2
5850.2.a.ci 2
5850.2.a.cj 2
5850.2.a.ck 2
5850.2.a.cl 2
5850.2.a.cm 2
5850.2.a.cn 2
5850.2.a.co 3
5850.2.a.cp 3
5850.2.a.cq 3
5850.2.a.cr 3
5850.2.a.cs 3
5850.2.a.ct 3
5850.2.b \(\chi_{5850}(1351, \cdot)\) n/a 110 1
5850.2.e \(\chi_{5850}(5149, \cdot)\) 5850.2.e.a 2 1
5850.2.e.b 2
5850.2.e.c 2
5850.2.e.d 2
5850.2.e.e 2
5850.2.e.f 2
5850.2.e.g 2
5850.2.e.h 2
5850.2.e.i 2
5850.2.e.j 2
5850.2.e.k 2
5850.2.e.l 2
5850.2.e.m 2
5850.2.e.n 2
5850.2.e.o 2
5850.2.e.p 2
5850.2.e.q 2
5850.2.e.r 2
5850.2.e.s 2
5850.2.e.t 2
5850.2.e.u 2
5850.2.e.v 2
5850.2.e.w 2
5850.2.e.x 2
5850.2.e.y 2
5850.2.e.z 2
5850.2.e.ba 2
5850.2.e.bb 2
5850.2.e.bc 2
5850.2.e.bd 2
5850.2.e.be 2
5850.2.e.bf 2
5850.2.e.bg 2
5850.2.e.bh 4
5850.2.e.bi 4
5850.2.e.bj 4
5850.2.e.bk 4
5850.2.e.bl 4
5850.2.e.bm 4
5850.2.f \(\chi_{5850}(649, \cdot)\) n/a 104 1
5850.2.i \(\chi_{5850}(451, \cdot)\) n/a 222 2
5850.2.j \(\chi_{5850}(1951, \cdot)\) n/a 456 2
5850.2.k \(\chi_{5850}(601, \cdot)\) n/a 532 2
5850.2.l \(\chi_{5850}(2401, \cdot)\) n/a 532 2
5850.2.m \(\chi_{5850}(1243, \cdot)\) n/a 210 2
5850.2.o \(\chi_{5850}(1457, \cdot)\) n/a 144 2
5850.2.q \(\chi_{5850}(1799, \cdot)\) n/a 168 2
5850.2.s \(\chi_{5850}(2501, \cdot)\) n/a 172 2
5850.2.v \(\chi_{5850}(2807, \cdot)\) n/a 168 2
5850.2.w \(\chi_{5850}(307, \cdot)\) n/a 210 2
5850.2.y \(\chi_{5850}(1171, \cdot)\) n/a 600 4
5850.2.z \(\chi_{5850}(1699, \cdot)\) n/a 504 2
5850.2.bc \(\chi_{5850}(751, \cdot)\) n/a 532 2
5850.2.be \(\chi_{5850}(3949, \cdot)\) n/a 504 2
5850.2.bh \(\chi_{5850}(2599, \cdot)\) n/a 504 2
5850.2.bk \(\chi_{5850}(199, \cdot)\) n/a 208 2
5850.2.bn \(\chi_{5850}(4651, \cdot)\) n/a 532 2
5850.2.bp \(\chi_{5850}(1249, \cdot)\) n/a 432 2
5850.2.bq \(\chi_{5850}(3799, \cdot)\) n/a 212 2
5850.2.bt \(\chi_{5850}(901, \cdot)\) n/a 224 2
5850.2.bu \(\chi_{5850}(3301, \cdot)\) n/a 532 2
5850.2.bw \(\chi_{5850}(3649, \cdot)\) n/a 504 2
5850.2.ca \(\chi_{5850}(49, \cdot)\) n/a 504 2
5850.2.cb \(\chi_{5850}(469, \cdot)\) n/a 600 4
5850.2.ce \(\chi_{5850}(181, \cdot)\) n/a 696 4
5850.2.ch \(\chi_{5850}(1819, \cdot)\) n/a 704 4
5850.2.cj \(\chi_{5850}(193, \cdot)\) n/a 1008 4
5850.2.ck \(\chi_{5850}(643, \cdot)\) n/a 1008 4
5850.2.cn \(\chi_{5850}(1207, \cdot)\) n/a 420 4
5850.2.co \(\chi_{5850}(2257, \cdot)\) n/a 1008 4
5850.2.cr \(\chi_{5850}(3857, \cdot)\) n/a 1008 4
5850.2.ct \(\chi_{5850}(2357, \cdot)\) n/a 336 4
5850.2.cu \(\chi_{5850}(257, \cdot)\) n/a 1008 4
5850.2.cx \(\chi_{5850}(857, \cdot)\) n/a 1008 4
5850.2.cz \(\chi_{5850}(749, \cdot)\) n/a 1008 4
5850.2.da \(\chi_{5850}(851, \cdot)\) n/a 1064 4
5850.2.dc \(\chi_{5850}(1151, \cdot)\) n/a 360 4
5850.2.df \(\chi_{5850}(401, \cdot)\) n/a 1064 4
5850.2.dh \(\chi_{5850}(2099, \cdot)\) n/a 1008 4
5850.2.di \(\chi_{5850}(149, \cdot)\) n/a 1008 4
5850.2.dk \(\chi_{5850}(449, \cdot)\) n/a 336 4
5850.2.dn \(\chi_{5850}(551, \cdot)\) n/a 1064 4
5850.2.do \(\chi_{5850}(443, \cdot)\) n/a 864 4
5850.2.dr \(\chi_{5850}(893, \cdot)\) n/a 1008 4
5850.2.ds \(\chi_{5850}(107, \cdot)\) n/a 336 4
5850.2.du \(\chi_{5850}(2207, \cdot)\) n/a 1008 4
5850.2.dw \(\chi_{5850}(457, \cdot)\) n/a 1008 4
5850.2.dz \(\chi_{5850}(1357, \cdot)\) n/a 1008 4
5850.2.ea \(\chi_{5850}(1657, \cdot)\) n/a 420 4
5850.2.ed \(\chi_{5850}(7, \cdot)\) n/a 1008 4
5850.2.ee \(\chi_{5850}(841, \cdot)\) n/a 3360 8
5850.2.ef \(\chi_{5850}(391, \cdot)\) n/a 2880 8
5850.2.eg \(\chi_{5850}(991, \cdot)\) n/a 1408 8
5850.2.eh \(\chi_{5850}(61, \cdot)\) n/a 3360 8
5850.2.ej \(\chi_{5850}(73, \cdot)\) n/a 1400 8
5850.2.ek \(\chi_{5850}(233, \cdot)\) n/a 1120 8
5850.2.en \(\chi_{5850}(161, \cdot)\) n/a 1120 8
5850.2.ep \(\chi_{5850}(359, \cdot)\) n/a 1120 8
5850.2.er \(\chi_{5850}(53, \cdot)\) n/a 960 8
5850.2.et \(\chi_{5850}(1477, \cdot)\) n/a 1400 8
5850.2.eu \(\chi_{5850}(511, \cdot)\) n/a 3360 8
5850.2.ex \(\chi_{5850}(529, \cdot)\) n/a 3360 8
5850.2.ez \(\chi_{5850}(829, \cdot)\) n/a 1408 8
5850.2.fc \(\chi_{5850}(259, \cdot)\) n/a 3360 8
5850.2.ff \(\chi_{5850}(439, \cdot)\) n/a 3360 8
5850.2.fi \(\chi_{5850}(139, \cdot)\) n/a 3360 8
5850.2.fk \(\chi_{5850}(571, \cdot)\) n/a 3360 8
5850.2.fl \(\chi_{5850}(361, \cdot)\) n/a 1392 8
5850.2.fo \(\chi_{5850}(289, \cdot)\) n/a 1392 8
5850.2.fp \(\chi_{5850}(79, \cdot)\) n/a 2880 8
5850.2.fr \(\chi_{5850}(121, \cdot)\) n/a 3360 8
5850.2.ft \(\chi_{5850}(979, \cdot)\) n/a 3360 8
5850.2.fw \(\chi_{5850}(67, \cdot)\) n/a 6720 16
5850.2.fz \(\chi_{5850}(697, \cdot)\) n/a 6720 16
5850.2.ga \(\chi_{5850}(37, \cdot)\) n/a 2800 16
5850.2.gd \(\chi_{5850}(223, \cdot)\) n/a 6720 16
5850.2.gf \(\chi_{5850}(563, \cdot)\) n/a 6720 16
5850.2.gh \(\chi_{5850}(503, \cdot)\) n/a 2240 16
5850.2.gi \(\chi_{5850}(653, \cdot)\) n/a 6720 16
5850.2.gl \(\chi_{5850}(677, \cdot)\) n/a 5760 16
5850.2.gm \(\chi_{5850}(281, \cdot)\) n/a 6720 16
5850.2.gp \(\chi_{5850}(89, \cdot)\) n/a 2240 16
5850.2.gr \(\chi_{5850}(59, \cdot)\) n/a 6720 16
5850.2.gs \(\chi_{5850}(509, \cdot)\) n/a 6720 16
5850.2.gu \(\chi_{5850}(41, \cdot)\) n/a 6720 16
5850.2.gx \(\chi_{5850}(71, \cdot)\) n/a 2240 16
5850.2.gz \(\chi_{5850}(11, \cdot)\) n/a 6720 16
5850.2.ha \(\chi_{5850}(239, \cdot)\) n/a 6720 16
5850.2.hc \(\chi_{5850}(77, \cdot)\) n/a 6720 16
5850.2.hf \(\chi_{5850}(23, \cdot)\) n/a 6720 16
5850.2.hg \(\chi_{5850}(17, \cdot)\) n/a 2240 16
5850.2.hi \(\chi_{5850}(113, \cdot)\) n/a 6720 16
5850.2.hl \(\chi_{5850}(163, \cdot)\) n/a 2800 16
5850.2.hm \(\chi_{5850}(187, \cdot)\) n/a 6720 16
5850.2.hp \(\chi_{5850}(553, \cdot)\) n/a 6720 16
5850.2.hq \(\chi_{5850}(427, \cdot)\) n/a 6720 16

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(5850))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(5850)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(9))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(13))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(18))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(26))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(39))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(45))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(65))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(78))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(90))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(117))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(130))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(195))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(225))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(234))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(325))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(390))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(585))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(650))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(975))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1170))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1950))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2925))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5850))\)\(^{\oplus 1}\)