↑

Properties

Label 6900.2
Level 6900
Weight 2
Dimension 507316
Nonzero newspaces 48
Sturm bound 5068800

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 6900 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 23 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 48 \)
Sturm bound: \(5068800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6900))\).

Total New Old
Modular forms 1279520 510756 768764
Cusp forms 1254881 507316 747565
Eisenstein series 24639 3440 21199

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6900))\)

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
6900.2.a \(\chi_{6900}(1, \cdot)\) 6900.2.a.a 1 1
6900.2.a.b 1
6900.2.a.c 1
6900.2.a.d 1
6900.2.a.e 1
6900.2.a.f 1
6900.2.a.g 1
6900.2.a.h 1
6900.2.a.i 1
6900.2.a.j 2
6900.2.a.k 2
6900.2.a.l 2
6900.2.a.m 2
6900.2.a.n 2
6900.2.a.o 2
6900.2.a.p 2
6900.2.a.q 2
6900.2.a.r 2
6900.2.a.s 2
6900.2.a.t 2
6900.2.a.u 2
6900.2.a.v 2
6900.2.a.w 2
6900.2.a.x 3
6900.2.a.y 3
6900.2.a.z 3
6900.2.a.ba 4
6900.2.a.bb 4
6900.2.a.bc 7
6900.2.a.bd 7
6900.2.f \(\chi_{6900}(6349, \cdot)\) 6900.2.f.a 2 1
6900.2.f.b 2
6900.2.f.c 2
6900.2.f.d 2
6900.2.f.e 2
6900.2.f.f 2
6900.2.f.g 2
6900.2.f.h 4
6900.2.f.i 4
6900.2.f.j 4
6900.2.f.k 4
6900.2.f.l 4
6900.2.f.m 4
6900.2.f.n 4
6900.2.f.o 4
6900.2.f.p 4
6900.2.f.q 4
6900.2.f.r 6
6900.2.f.s 8
6900.2.g \(\chi_{6900}(2299, \cdot)\) n/a 432 1
6900.2.h \(\chi_{6900}(1151, \cdot)\) n/a 836 1
6900.2.i \(\chi_{6900}(4001, \cdot)\) n/a 152 1
6900.2.n \(\chi_{6900}(3449, \cdot)\) n/a 144 1
6900.2.o \(\chi_{6900}(599, \cdot)\) n/a 792 1
6900.2.p \(\chi_{6900}(2851, \cdot)\) n/a 456 1
6900.2.q \(\chi_{6900}(2207, \cdot)\) n/a 1712 2
6900.2.r \(\chi_{6900}(2393, \cdot)\) n/a 264 2
6900.2.s \(\chi_{6900}(1243, \cdot)\) n/a 792 2
6900.2.t \(\chi_{6900}(1057, \cdot)\) n/a 144 2
6900.2.y \(\chi_{6900}(1381, \cdot)\) n/a 448 4
6900.2.z \(\chi_{6900}(1241, \cdot)\) n/a 960 4
6900.2.ba \(\chi_{6900}(2531, \cdot)\) n/a 5280 4
6900.2.bb \(\chi_{6900}(919, \cdot)\) n/a 2880 4
6900.2.bc \(\chi_{6900}(829, \cdot)\) n/a 432 4
6900.2.bh \(\chi_{6900}(91, \cdot)\) n/a 2880 4
6900.2.bi \(\chi_{6900}(1979, \cdot)\) n/a 5280 4
6900.2.bj \(\chi_{6900}(689, \cdot)\) n/a 960 4
6900.2.bo \(\chi_{6900}(301, \cdot)\) n/a 760 10
6900.2.bt \(\chi_{6900}(1333, \cdot)\) n/a 960 8
6900.2.bu \(\chi_{6900}(967, \cdot)\) n/a 5280 8
6900.2.bv \(\chi_{6900}(737, \cdot)\) n/a 1760 8
6900.2.bw \(\chi_{6900}(827, \cdot)\) n/a 11456 8
6900.2.bx \(\chi_{6900}(451, \cdot)\) n/a 4560 10
6900.2.by \(\chi_{6900}(899, \cdot)\) n/a 8560 10
6900.2.bz \(\chi_{6900}(149, \cdot)\) n/a 1440 10
6900.2.ce \(\chi_{6900}(401, \cdot)\) n/a 1520 10
6900.2.cf \(\chi_{6900}(1451, \cdot)\) n/a 9000 10
6900.2.cg \(\chi_{6900}(199, \cdot)\) n/a 4320 10
6900.2.ch \(\chi_{6900}(49, \cdot)\) n/a 720 10
6900.2.cq \(\chi_{6900}(157, \cdot)\) n/a 1440 20
6900.2.cr \(\chi_{6900}(307, \cdot)\) n/a 8640 20
6900.2.cs \(\chi_{6900}(257, \cdot)\) n/a 2880 20
6900.2.ct \(\chi_{6900}(107, \cdot)\) n/a 17120 20
6900.2.cu \(\chi_{6900}(121, \cdot)\) n/a 4800 40
6900.2.cz \(\chi_{6900}(89, \cdot)\) n/a 9600 40
6900.2.da \(\chi_{6900}(59, \cdot)\) n/a 57280 40
6900.2.db \(\chi_{6900}(511, \cdot)\) n/a 28800 40
6900.2.dg \(\chi_{6900}(169, \cdot)\) n/a 4800 40
6900.2.dh \(\chi_{6900}(19, \cdot)\) n/a 28800 40
6900.2.di \(\chi_{6900}(71, \cdot)\) n/a 57280 40
6900.2.dj \(\chi_{6900}(221, \cdot)\) n/a 9600 40
6900.2.dk \(\chi_{6900}(83, \cdot)\) n/a 114560 80
6900.2.dl \(\chi_{6900}(77, \cdot)\) n/a 19200 80
6900.2.dm \(\chi_{6900}(127, \cdot)\) n/a 57600 80
6900.2.dn \(\chi_{6900}(37, \cdot)\) n/a 9600 80

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6900))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6900)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 36}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(12))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(15))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(23))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(30))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(46))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(60))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(69))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(75))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(92))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(115))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(138))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(230))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(276))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(345))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(460))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(575))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(690))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1150))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1380))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1725))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2300))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3450))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(6900))\)\(^{\oplus 1}\)