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Properties

Label 8092.2
Level 8092
Weight 2
Dimension 1105296
Nonzero newspaces 40
Sturm bound 7990272

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Defining parameters

Level: \( N \) = \( 8092 = 2^{2} \cdot 7 \cdot 17^{2} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 40 \)
Sturm bound: \(7990272\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8092))\).

Total New Old
Modular forms 2009568 1112668 896900
Cusp forms 1985569 1105296 880273
Eisenstein series 23999 7372 16627

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8092))\)

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
8092.2.a \(\chi_{8092}(1, \cdot)\) 8092.2.a.a 1 1
8092.2.a.b 1
8092.2.a.c 1
8092.2.a.d 1
8092.2.a.e 1
8092.2.a.f 1
8092.2.a.g 1
8092.2.a.h 1
8092.2.a.i 1
8092.2.a.j 1
8092.2.a.k 2
8092.2.a.l 2
8092.2.a.m 2
8092.2.a.n 2
8092.2.a.o 3
8092.2.a.p 3
8092.2.a.q 4
8092.2.a.r 4
8092.2.a.s 8
8092.2.a.t 8
8092.2.a.u 12
8092.2.a.v 12
8092.2.a.w 12
8092.2.a.x 12
8092.2.a.y 20
8092.2.a.z 20
8092.2.b \(\chi_{8092}(6357, \cdot)\) n/a 136 1
8092.2.e \(\chi_{8092}(8091, \cdot)\) n/a 1052 1
8092.2.f \(\chi_{8092}(1735, \cdot)\) n/a 1054 1
8092.2.i \(\chi_{8092}(1157, \cdot)\) n/a 362 2
8092.2.k \(\chi_{8092}(251, \cdot)\) n/a 2104 2
8092.2.l \(\chi_{8092}(6609, \cdot)\) n/a 272 2
8092.2.p \(\chi_{8092}(579, \cdot)\) n/a 2108 2
8092.2.q \(\chi_{8092}(4623, \cdot)\) n/a 2104 2
8092.2.t \(\chi_{8092}(1733, \cdot)\) n/a 360 2
8092.2.u \(\chi_{8092}(757, \cdot)\) n/a 536 4
8092.2.w \(\chi_{8092}(2491, \cdot)\) n/a 4208 4
8092.2.z \(\chi_{8092}(327, \cdot)\) n/a 4208 4
8092.2.ba \(\chi_{8092}(905, \cdot)\) n/a 720 4
8092.2.bd \(\chi_{8092}(827, \cdot)\) n/a 6480 8
8092.2.be \(\chi_{8092}(2561, \cdot)\) n/a 1440 8
8092.2.bg \(\chi_{8092}(477, \cdot)\) n/a 2432 16
8092.2.bi \(\chi_{8092}(977, \cdot)\) n/a 1440 8
8092.2.bk \(\chi_{8092}(423, \cdot)\) n/a 8416 8
8092.2.bn \(\chi_{8092}(307, \cdot)\) n/a 19520 16
8092.2.bo \(\chi_{8092}(475, \cdot)\) n/a 19520 16
8092.2.br \(\chi_{8092}(169, \cdot)\) n/a 2432 16
8092.2.bt \(\chi_{8092}(1025, \cdot)\) n/a 2880 16
8092.2.bu \(\chi_{8092}(907, \cdot)\) n/a 16832 16
8092.2.bw \(\chi_{8092}(137, \cdot)\) n/a 6528 32
8092.2.by \(\chi_{8092}(225, \cdot)\) n/a 4864 32
8092.2.bz \(\chi_{8092}(55, \cdot)\) n/a 39040 32
8092.2.cb \(\chi_{8092}(305, \cdot)\) n/a 6528 32
8092.2.ce \(\chi_{8092}(271, \cdot)\) n/a 39040 32
8092.2.cf \(\chi_{8092}(103, \cdot)\) n/a 39040 32
8092.2.cj \(\chi_{8092}(83, \cdot)\) n/a 78080 64
8092.2.cl \(\chi_{8092}(253, \cdot)\) n/a 9856 64
8092.2.cn \(\chi_{8092}(81, \cdot)\) n/a 13056 64
8092.2.co \(\chi_{8092}(47, \cdot)\) n/a 78080 64
8092.2.cr \(\chi_{8092}(41, \cdot)\) n/a 26112 128
8092.2.cs \(\chi_{8092}(71, \cdot)\) n/a 117504 128
8092.2.cu \(\chi_{8092}(19, \cdot)\) n/a 156160 128
8092.2.cw \(\chi_{8092}(9, \cdot)\) n/a 26112 128
8092.2.cz \(\chi_{8092}(11, \cdot)\) n/a 312320 256
8092.2.da \(\chi_{8092}(5, \cdot)\) n/a 52224 256

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8092))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8092)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(7))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(14))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(17))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(28))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(34))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(68))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(119))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(238))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(289))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(476))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(578))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1156))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2023))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4046))\)\(^{\oplus 2}\)