# Properties

 Label 8005.2 Level 8005 Weight 2 Dimension 2.3448e+06 Nonzero newspaces 42 Sturm bound 1.02528e+07

## 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

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