Properties

Label 8005.2
Level 8005
Weight 2
Dimension 2344799
Nonzero newspaces 42
Sturm bound 10252800

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Defining parameters

Level: \( N \) = \( 8005\( 8005 = 5 \cdot 1601 \) \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 42 \)
Sturm bound: \(10252800\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8005))\).

Total New Old
Modular forms 2569600 2354395 215205
Cusp forms 2556801 2344799 212002
Eisenstein series 12799 9596 3203

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8005))\)

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 the newforms together with their dimension.

Label \(\chi\) Newforms Dimension \(\chi\) degree
8005.2.a \(\chi_{8005}(1, \cdot)\) 8005.2.a.a 1 1
8005.2.a.b 1
8005.2.a.c 2
8005.2.a.d 2
8005.2.a.e 126
8005.2.a.f 127
8005.2.a.g 137
8005.2.a.h 137
8005.2.b \(\chi_{8005}(4804, \cdot)\) n/a 800 1
8005.2.c \(\chi_{8005}(8004, \cdot)\) n/a 800 1
8005.2.d \(\chi_{8005}(3201, \cdot)\) n/a 534 1
8005.2.e \(\chi_{8005}(6364, \cdot)\) n/a 1600 2
8005.2.j \(\chi_{8005}(1561, \cdot)\) n/a 1068 2
8005.2.k \(\chi_{8005}(4966, \cdot)\) n/a 2136 4
8005.2.l \(\chi_{8005}(1291, \cdot)\) n/a 2136 4
8005.2.o \(\chi_{8005}(2009, \cdot)\) n/a 3200 4
8005.2.p \(\chi_{8005}(4361, \cdot)\) n/a 2136 4
8005.2.q \(\chi_{8005}(1159, \cdot)\) n/a 3200 4
8005.2.r \(\chi_{8005}(1764, \cdot)\) n/a 3200 4
8005.2.t \(\chi_{8005}(674, \cdot)\) n/a 6400 8
8005.2.u \(\chi_{8005}(791, \cdot)\) n/a 4272 8
8005.2.w \(\chi_{8005}(116, \cdot)\) n/a 4272 8
8005.2.bb \(\chi_{8005}(69, \cdot)\) n/a 6400 8
8005.2.bc \(\chi_{8005}(361, \cdot)\) n/a 10680 20
8005.2.bf \(\chi_{8005}(109, \cdot)\) n/a 12768 16
8005.2.bg \(\chi_{8005}(206, \cdot)\) n/a 8544 16
8005.2.bh \(\chi_{8005}(219, \cdot)\) n/a 12800 16
8005.2.bk \(\chi_{8005}(666, \cdot)\) n/a 8544 16
8005.2.bl \(\chi_{8005}(394, \cdot)\) n/a 16000 20
8005.2.bm \(\chi_{8005}(61, \cdot)\) n/a 10680 20
8005.2.bn \(\chi_{8005}(19, \cdot)\) n/a 16000 20
8005.2.bo \(\chi_{8005}(13, \cdot)\) n/a 25568 32
8005.2.bp \(\chi_{8005}(137, \cdot)\) n/a 25568 32
8005.2.bt \(\chi_{8005}(314, \cdot)\) n/a 25600 32
8005.2.bu \(\chi_{8005}(321, \cdot)\) n/a 17088 32
8005.2.bx \(\chi_{8005}(16, \cdot)\) n/a 21360 40
8005.2.ca \(\chi_{8005}(299, \cdot)\) n/a 32000 40
8005.2.cc \(\chi_{8005}(119, \cdot)\) n/a 51072 64
8005.2.cd \(\chi_{8005}(156, \cdot)\) n/a 34176 64
8005.2.cg \(\chi_{8005}(4, \cdot)\) n/a 64000 80
8005.2.cj \(\chi_{8005}(76, \cdot)\) n/a 42720 80
8005.2.cm \(\chi_{8005}(12, \cdot)\) n/a 102272 128
8005.2.cn \(\chi_{8005}(83, \cdot)\) n/a 102272 128
8005.2.cp \(\chi_{8005}(21, \cdot)\) n/a 85440 160
8005.2.cq \(\chi_{8005}(84, \cdot)\) n/a 128000 160
8005.2.cs \(\chi_{8005}(36, \cdot)\) n/a 170880 320
8005.2.cv \(\chi_{8005}(9, \cdot)\) n/a 255360 320
8005.2.cx \(\chi_{8005}(23, \cdot)\) n/a 511360 640
8005.2.cy \(\chi_{8005}(3, \cdot)\) n/a 511360 640

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8005))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8005)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(1601))\)\(^{\oplus 2}\)

Hecke characteristic polynomials

$p$ $F_p(T)$
$2$ (\( 1 + T + 2 T^{2} \))(\( 1 + T + 2 T^{2} \))(\( 1 + T + 3 T^{2} + 2 T^{3} + 4 T^{4} \))(\( ( 1 - T + 2 T^{2} )^{2} \))
$3$ (\( 1 + 2 T + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))(\( ( 1 + T + 3 T^{2} )^{2} \))(\( 1 + 4 T^{2} + 9 T^{4} \))
$5$ (\( 1 - T \))(\( 1 - T \))(\( ( 1 - T )^{2} \))(\( ( 1 + T )^{2} \))
$7$ (\( 1 - 2 T + 7 T^{2} \))(\( 1 - 2 T + 7 T^{2} \))(\( 1 + 3 T + 15 T^{2} + 21 T^{3} + 49 T^{4} \))(\( 1 + 12 T^{2} + 49 T^{4} \))
$11$ (\( 1 + 6 T + 11 T^{2} \))(\( 1 + 11 T^{2} \))(\( 1 + 8 T + 33 T^{2} + 88 T^{3} + 121 T^{4} \))(\( 1 + 4 T + 8 T^{2} + 44 T^{3} + 121 T^{4} \))
$13$ (\( 1 + 2 T + 13 T^{2} \))(\( 1 + 4 T + 13 T^{2} \))(\( 1 + 8 T + 37 T^{2} + 104 T^{3} + 169 T^{4} \))(\( 1 - 6 T^{2} + 169 T^{4} \))
$17$ (\( 1 - 6 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 - 2 T + 15 T^{2} - 34 T^{3} + 289 T^{4} \))(\( 1 + 26 T^{2} + 289 T^{4} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 + 4 T + 19 T^{2} \))(\( 1 + 3 T + 39 T^{2} + 57 T^{3} + 361 T^{4} \))(\( ( 1 + 19 T^{2} )^{2} \))
$23$ (\( 1 - 2 T + 23 T^{2} \))(\( 1 + 2 T + 23 T^{2} \))(\( 1 + 11 T + 65 T^{2} + 253 T^{3} + 529 T^{4} \))(\( 1 + 8 T + 44 T^{2} + 184 T^{3} + 529 T^{4} \))
$29$ (\( 1 - 2 T + 29 T^{2} \))(\( 1 - 2 T + 29 T^{2} \))(\( 1 + 8 T + 69 T^{2} + 232 T^{3} + 841 T^{4} \))(\( ( 1 - 8 T + 29 T^{2} )^{2} \))
$31$ (\( 1 + 8 T + 31 T^{2} \))(\( 1 - 8 T + 31 T^{2} \))(\( ( 1 + 2 T + 31 T^{2} )^{2} \))(\( 1 - 8 T + 70 T^{2} - 248 T^{3} + 961 T^{4} \))
$37$ (\( 1 - 2 T + 37 T^{2} \))(\( 1 + 10 T + 37 T^{2} \))(\( 1 + 18 T + 150 T^{2} + 666 T^{3} + 1369 T^{4} \))(\( 1 + 2 T^{2} + 1369 T^{4} \))
$41$ (\( 1 + 6 T + 41 T^{2} \))(\( 1 - 6 T + 41 T^{2} \))(\( 1 + 4 T + 81 T^{2} + 164 T^{3} + 1681 T^{4} \))(\( ( 1 + 2 T + 41 T^{2} )^{2} \))
$43$ (\( 1 - 8 T + 43 T^{2} \))(\( 1 + 4 T + 43 T^{2} \))(\( 1 - 7 T + 97 T^{2} - 301 T^{3} + 1849 T^{4} \))(\( ( 1 + 8 T + 43 T^{2} )^{2} \))
$47$ (\( 1 - 12 T + 47 T^{2} \))(\( 1 - 4 T + 47 T^{2} \))(\( 1 + 89 T^{2} + 2209 T^{4} \))(\( 1 + 86 T^{2} + 2209 T^{4} \))
$53$ (\( 1 + 6 T + 53 T^{2} \))(\( 1 + 6 T + 53 T^{2} \))(\( 1 + 13 T + 147 T^{2} + 689 T^{3} + 2809 T^{4} \))(\( 1 - 16 T + 162 T^{2} - 848 T^{3} + 2809 T^{4} \))
$59$ (\( 1 - 10 T + 59 T^{2} \))(\( 1 - 12 T + 59 T^{2} \))(\( 1 + 22 T + 234 T^{2} + 1298 T^{3} + 3481 T^{4} \))(\( 1 + 4 T - 40 T^{2} + 236 T^{3} + 3481 T^{4} \))
$61$ (\( 1 + 2 T + 61 T^{2} \))(\( 1 + 14 T + 61 T^{2} \))(\( 1 + 77 T^{2} + 3721 T^{4} \))(\( 1 + 12 T + 126 T^{2} + 732 T^{3} + 3721 T^{4} \))
$67$ (\( 1 + 8 T + 67 T^{2} \))(\( 1 + 4 T + 67 T^{2} \))(\( ( 1 + 9 T + 67 T^{2} )^{2} \))(\( 1 + 8 T + 118 T^{2} + 536 T^{3} + 4489 T^{4} \))
$71$ (\( 1 - 10 T + 71 T^{2} \))(\( 1 - 12 T + 71 T^{2} \))(\( 1 + 25 T + 297 T^{2} + 1775 T^{3} + 5041 T^{4} \))(\( 1 + 12 T + 176 T^{2} + 852 T^{3} + 5041 T^{4} \))
$73$ (\( 1 + 2 T + 73 T^{2} \))(\( 1 + 8 T + 73 T^{2} \))(\( 1 - 4 T + 105 T^{2} - 292 T^{3} + 5329 T^{4} \))(\( 1 + 8 T + 154 T^{2} + 584 T^{3} + 5329 T^{4} \))
$79$ (\( 1 + 8 T + 79 T^{2} \))(\( 1 + 8 T + 79 T^{2} \))(\( 1 - 6 T + 42 T^{2} - 474 T^{3} + 6241 T^{4} \))(\( ( 1 - 12 T + 79 T^{2} )^{2} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))(\( 1 + 6 T + 83 T^{2} \))(\( 1 - 3 T + 167 T^{2} - 249 T^{3} + 6889 T^{4} \))(\( 1 + 16 T + 180 T^{2} + 1328 T^{3} + 6889 T^{4} \))
$89$ (\( 1 + 2 T + 89 T^{2} \))(\( 1 - 6 T + 89 T^{2} \))(\( 1 + T + 77 T^{2} + 89 T^{3} + 7921 T^{4} \))(\( 1 + 8 T + 162 T^{2} + 712 T^{3} + 7921 T^{4} \))
$97$ (\( 1 - 10 T + 97 T^{2} \))(\( 1 + 18 T + 97 T^{2} \))(\( 1 + 14 T + 223 T^{2} + 1358 T^{3} + 9409 T^{4} \))(\( 1 + 12 T + 102 T^{2} + 1164 T^{3} + 9409 T^{4} \))
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