Properties

Label 800.6
Level 800
Weight 6
Dimension 49565
Nonzero newspaces 20
Sturm bound 230400
Trace bound 7

Downloads

Learn more

Defining parameters

Level: \( N \) = \( 800 = 2^{5} \cdot 5^{2} \)
Weight: \( k \) = \( 6 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(230400\)
Trace bound: \(7\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(800))\).

Total New Old
Modular forms 96896 49975 46921
Cusp forms 95104 49565 45539
Eisenstein series 1792 410 1382

Trace form

\( 49565 q - 52 q^{2} - 40 q^{3} - 52 q^{4} - 64 q^{5} - 84 q^{6} - 136 q^{7} - 52 q^{8} + 209 q^{9} - 64 q^{10} - 64 q^{11} - 1636 q^{12} + 58 q^{13} + 2428 q^{14} - 48 q^{15} + 4096 q^{16} + 1786 q^{17}+ \cdots + 338496 q^{99}+O(q^{100}) \) Copy content Toggle raw display

Decomposition of \(S_{6}^{\mathrm{new}}(\Gamma_1(800))\)

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
800.6.a \(\chi_{800}(1, \cdot)\) 800.6.a.a 1 1
800.6.a.b 1
800.6.a.c 1
800.6.a.d 1
800.6.a.e 1
800.6.a.f 2
800.6.a.g 2
800.6.a.h 2
800.6.a.i 2
800.6.a.j 2
800.6.a.k 2
800.6.a.l 2
800.6.a.m 2
800.6.a.n 3
800.6.a.o 3
800.6.a.p 4
800.6.a.q 4
800.6.a.r 4
800.6.a.s 5
800.6.a.t 5
800.6.a.u 5
800.6.a.v 5
800.6.a.w 6
800.6.a.x 6
800.6.a.y 6
800.6.a.z 6
800.6.a.ba 6
800.6.a.bb 6
800.6.c \(\chi_{800}(449, \cdot)\) 800.6.c.a 2 1
800.6.c.b 2
800.6.c.c 2
800.6.c.d 4
800.6.c.e 4
800.6.c.f 4
800.6.c.g 4
800.6.c.h 4
800.6.c.i 4
800.6.c.j 6
800.6.c.k 6
800.6.c.l 8
800.6.c.m 8
800.6.c.n 10
800.6.c.o 10
800.6.c.p 12
800.6.d \(\chi_{800}(401, \cdot)\) 800.6.d.a 4 1
800.6.d.b 20
800.6.d.c 20
800.6.d.d 20
800.6.d.e 28
800.6.f \(\chi_{800}(49, \cdot)\) 800.6.f.a 8 1
800.6.f.b 20
800.6.f.c 20
800.6.f.d 40
800.6.j \(\chi_{800}(407, \cdot)\) None 0 2
800.6.l \(\chi_{800}(201, \cdot)\) None 0 2
800.6.n \(\chi_{800}(543, \cdot)\) n/a 180 2
800.6.o \(\chi_{800}(143, \cdot)\) n/a 176 2
800.6.q \(\chi_{800}(249, \cdot)\) None 0 2
800.6.s \(\chi_{800}(7, \cdot)\) None 0 2
800.6.u \(\chi_{800}(161, \cdot)\) n/a 600 4
800.6.v \(\chi_{800}(43, \cdot)\) n/a 1432 4
800.6.y \(\chi_{800}(101, \cdot)\) n/a 1508 4
800.6.ba \(\chi_{800}(149, \cdot)\) n/a 1432 4
800.6.bb \(\chi_{800}(107, \cdot)\) n/a 1432 4
800.6.be \(\chi_{800}(209, \cdot)\) n/a 592 4
800.6.bg \(\chi_{800}(129, \cdot)\) n/a 600 4
800.6.bj \(\chi_{800}(81, \cdot)\) n/a 592 4
800.6.bl \(\chi_{800}(23, \cdot)\) None 0 8
800.6.bm \(\chi_{800}(41, \cdot)\) None 0 8
800.6.bp \(\chi_{800}(47, \cdot)\) n/a 1184 8
800.6.bq \(\chi_{800}(63, \cdot)\) n/a 1200 8
800.6.bt \(\chi_{800}(9, \cdot)\) None 0 8
800.6.bu \(\chi_{800}(87, \cdot)\) None 0 8
800.6.bx \(\chi_{800}(67, \cdot)\) n/a 9568 16
800.6.by \(\chi_{800}(29, \cdot)\) n/a 9568 16
800.6.ca \(\chi_{800}(21, \cdot)\) n/a 9568 16
800.6.cd \(\chi_{800}(3, \cdot)\) n/a 9568 16

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

Decomposition of \(S_{6}^{\mathrm{old}}(\Gamma_1(800))\) into lower level spaces

\( S_{6}^{\mathrm{old}}(\Gamma_1(800)) \cong \) \(S_{6}^{\mathrm{new}}(\Gamma_1(1))\)\(^{\oplus 18}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(2))\)\(^{\oplus 15}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(4))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(5))\)\(^{\oplus 12}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(8))\)\(^{\oplus 9}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(10))\)\(^{\oplus 10}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(16))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(20))\)\(^{\oplus 8}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(25))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(32))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(40))\)\(^{\oplus 6}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(50))\)\(^{\oplus 5}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(80))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(100))\)\(^{\oplus 4}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(160))\)\(^{\oplus 2}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(200))\)\(^{\oplus 3}\)\(\oplus\)\(S_{6}^{\mathrm{new}}(\Gamma_1(400))\)\(^{\oplus 2}\)