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Properties

Label 8000.2
Level 8000
Weight 2
Dimension 992512
Nonzero newspaces 42
Sturm bound 7680000

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Defining parameters

Level: \( N \) = \( 8000 = 2^{6} \cdot 5^{3} \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(7680000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8000))\).

Total New Old
Modular forms 1932960 998144 934816
Cusp forms 1907041 992512 914529
Eisenstein series 25919 5632 20287

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8000))\)

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
8000.2.a \(\chi_{8000}(1, \cdot)\) 8000.2.a.a 2 1
8000.2.a.b 2
8000.2.a.c 2
8000.2.a.d 2
8000.2.a.e 2
8000.2.a.f 2
8000.2.a.g 2
8000.2.a.h 2
8000.2.a.i 2
8000.2.a.j 2
8000.2.a.k 2
8000.2.a.l 2
8000.2.a.m 2
8000.2.a.n 2
8000.2.a.o 2
8000.2.a.p 2
8000.2.a.q 2
8000.2.a.r 2
8000.2.a.s 2
8000.2.a.t 2
8000.2.a.u 2
8000.2.a.v 2
8000.2.a.w 2
8000.2.a.x 2
8000.2.a.y 4
8000.2.a.z 4
8000.2.a.ba 4
8000.2.a.bb 4
8000.2.a.bc 4
8000.2.a.bd 4
8000.2.a.be 4
8000.2.a.bf 4
8000.2.a.bg 4
8000.2.a.bh 4
8000.2.a.bi 4
8000.2.a.bj 4
8000.2.a.bk 4
8000.2.a.bl 4
8000.2.a.bm 4
8000.2.a.bn 4
8000.2.a.bo 4
8000.2.a.bp 4
8000.2.a.bq 4
8000.2.a.br 4
8000.2.a.bs 4
8000.2.a.bt 4
8000.2.a.bu 6
8000.2.a.bv 6
8000.2.a.bw 6
8000.2.a.bx 6
8000.2.a.by 8
8000.2.a.bz 8
8000.2.a.ca 8
8000.2.a.cb 8
8000.2.c \(\chi_{8000}(5249, \cdot)\) n/a 192 1
8000.2.d \(\chi_{8000}(4001, \cdot)\) n/a 192 1
8000.2.f \(\chi_{8000}(1249, \cdot)\) n/a 192 1
8000.2.j \(\chi_{8000}(4943, \cdot)\) n/a 384 2
8000.2.l \(\chi_{8000}(2001, \cdot)\) n/a 384 2
8000.2.n \(\chi_{8000}(2943, \cdot)\) n/a 384 2
8000.2.o \(\chi_{8000}(3807, \cdot)\) n/a 384 2
8000.2.q \(\chi_{8000}(3249, \cdot)\) n/a 384 2
8000.2.s \(\chi_{8000}(943, \cdot)\) n/a 384 2
8000.2.u \(\chi_{8000}(1601, \cdot)\) n/a 696 4
8000.2.v \(\chi_{8000}(2807, \cdot)\) None 0 4
8000.2.y \(\chi_{8000}(1001, \cdot)\) None 0 4
8000.2.ba \(\chi_{8000}(249, \cdot)\) None 0 4
8000.2.bb \(\chi_{8000}(807, \cdot)\) None 0 4
8000.2.be \(\chi_{8000}(2849, \cdot)\) n/a 720 4
8000.2.bg \(\chi_{8000}(449, \cdot)\) n/a 696 4
8000.2.bj \(\chi_{8000}(801, \cdot)\) n/a 720 4
8000.2.bl \(\chi_{8000}(307, \cdot)\) n/a 6144 8
8000.2.bm \(\chi_{8000}(501, \cdot)\) n/a 6144 8
8000.2.bn \(\chi_{8000}(749, \cdot)\) n/a 6144 8
8000.2.br \(\chi_{8000}(1307, \cdot)\) n/a 6144 8
8000.2.bt \(\chi_{8000}(207, \cdot)\) n/a 1392 8
8000.2.bu \(\chi_{8000}(401, \cdot)\) n/a 1392 8
8000.2.bx \(\chi_{8000}(543, \cdot)\) n/a 1440 8
8000.2.by \(\chi_{8000}(1343, \cdot)\) n/a 1392 8
8000.2.cb \(\chi_{8000}(49, \cdot)\) n/a 1392 8
8000.2.cc \(\chi_{8000}(143, \cdot)\) n/a 1392 8
8000.2.ce \(\chi_{8000}(321, \cdot)\) n/a 5960 20
8000.2.cg \(\chi_{8000}(407, \cdot)\) None 0 16
8000.2.ch \(\chi_{8000}(649, \cdot)\) None 0 16
8000.2.cj \(\chi_{8000}(201, \cdot)\) None 0 16
8000.2.cm \(\chi_{8000}(7, \cdot)\) None 0 16
8000.2.cp \(\chi_{8000}(161, \cdot)\) n/a 6000 20
8000.2.cr \(\chi_{8000}(289, \cdot)\) n/a 6000 20
8000.2.cs \(\chi_{8000}(129, \cdot)\) n/a 5960 20
8000.2.cu \(\chi_{8000}(107, \cdot)\) n/a 22848 32
8000.2.cy \(\chi_{8000}(149, \cdot)\) n/a 22848 32
8000.2.cz \(\chi_{8000}(101, \cdot)\) n/a 22848 32
8000.2.da \(\chi_{8000}(43, \cdot)\) n/a 22848 32
8000.2.dd \(\chi_{8000}(209, \cdot)\) n/a 11920 40
8000.2.de \(\chi_{8000}(47, \cdot)\) n/a 11920 40
8000.2.dh \(\chi_{8000}(223, \cdot)\) n/a 12000 40
8000.2.di \(\chi_{8000}(63, \cdot)\) n/a 11920 40
8000.2.dl \(\chi_{8000}(303, \cdot)\) n/a 11920 40
8000.2.dm \(\chi_{8000}(81, \cdot)\) n/a 11920 40
8000.2.do \(\chi_{8000}(23, \cdot)\) None 0 80
8000.2.dq \(\chi_{8000}(9, \cdot)\) None 0 80
8000.2.dt \(\chi_{8000}(41, \cdot)\) None 0 80
8000.2.dv \(\chi_{8000}(87, \cdot)\) None 0 80
8000.2.dw \(\chi_{8000}(67, \cdot)\) n/a 191680 160
8000.2.dz \(\chi_{8000}(29, \cdot)\) n/a 191680 160
8000.2.eb \(\chi_{8000}(21, \cdot)\) n/a 191680 160
8000.2.ec \(\chi_{8000}(3, \cdot)\) n/a 191680 160

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8000))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8000)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 28}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 24}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 20}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 21}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 16}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 18}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 15}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 14}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 12}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(64))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 9}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 10}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(125))\)\(^{\oplus 7}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 8}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(250))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(320))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 6}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(500))\)\(^{\oplus 5}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(800))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1000))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1600))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(2000))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(4000))\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(8000))\)\(^{\oplus 1}\)