# Properties

 Label 8007.2 Level 8007 Weight 2 Dimension 1.75754e+06 Nonzero newspaces 72 Sturm bound 9.46483e+06

## Defining parameters

 Level: $$N$$ = $$8007 = 3 \cdot 17 \cdot 157$$ Weight: $$k$$ = $$2$$ Nonzero newspaces: $$72$$ Sturm bound: $$9464832$$

## Dimensions

The following table gives the dimensions of various subspaces of $$M_{2}(\Gamma_1(8007))$$.

Total New Old
Modular forms 2376192 1766839 609353
Cusp forms 2356225 1757543 598682
Eisenstein series 19967 9296 10671

## Decomposition of $$S_{2}^{\mathrm{new}}(\Gamma_1(8007))$$

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
8007.2.a $$\chi_{8007}(1, \cdot)$$ 8007.2.a.a 1 1
8007.2.a.b 2
8007.2.a.c 39
8007.2.a.d 40
8007.2.a.e 46
8007.2.a.f 48
8007.2.a.g 56
8007.2.a.h 56
8007.2.a.i 63
8007.2.a.j 64
8007.2.b $$\chi_{8007}(4081, \cdot)$$ n/a 420 1
8007.2.e $$\chi_{8007}(2668, \cdot)$$ n/a 472 1
8007.2.f $$\chi_{8007}(6595, \cdot)$$ n/a 468 1
8007.2.i $$\chi_{8007}(1582, \cdot)$$ n/a 844 2
8007.2.k $$\chi_{8007}(472, \cdot)$$ n/a 936 2
8007.2.m $$\chi_{8007}(6566, \cdot)$$ n/a 1888 2
8007.2.n $$\chi_{8007}(443, \cdot)$$ n/a 1688 2
8007.2.q $$\chi_{8007}(4895, \cdot)$$ n/a 1888 2
8007.2.r $$\chi_{8007}(914, \cdot)$$ n/a 1888 2
8007.2.u $$\chi_{8007}(2197, \cdot)$$ n/a 944 2
8007.2.w $$\chi_{8007}(1087, \cdot)$$ n/a 944 2
8007.2.x $$\chi_{8007}(2500, \cdot)$$ n/a 844 2
8007.2.ba $$\chi_{8007}(169, \cdot)$$ n/a 952 2
8007.2.bc $$\chi_{8007}(185, \cdot)$$ n/a 3776 4
8007.2.bg $$\chi_{8007}(943, \cdot)$$ n/a 1872 4
8007.2.bh $$\chi_{8007}(784, \cdot)$$ n/a 1904 4
8007.2.bi $$\chi_{8007}(2327, \cdot)$$ n/a 3776 4
8007.2.bk $$\chi_{8007}(2053, \cdot)$$ n/a 1904 4
8007.2.bm $$\chi_{8007}(650, \cdot)$$ n/a 3776 4
8007.2.bo $$\chi_{8007}(50, \cdot)$$ n/a 3776 4
8007.2.br $$\chi_{8007}(1463, \cdot)$$ n/a 3368 4
8007.2.bt $$\chi_{8007}(2333, \cdot)$$ n/a 3776 4
8007.2.bu $$\chi_{8007}(13, \cdot)$$ n/a 1888 4
8007.2.bw $$\chi_{8007}(256, \cdot)$$ n/a 5040 12
8007.2.by $$\chi_{8007}(470, \cdot)$$ n/a 7552 8
8007.2.bz $$\chi_{8007}(158, \cdot)$$ n/a 7488 8
8007.2.cb $$\chi_{8007}(2170, \cdot)$$ n/a 3792 8
8007.2.ce $$\chi_{8007}(28, \cdot)$$ n/a 3792 8
8007.2.cg $$\chi_{8007}(1862, \cdot)$$ n/a 7552 8
8007.2.ch $$\chi_{8007}(145, \cdot)$$ n/a 3808 8
8007.2.ci $$\chi_{8007}(1243, \cdot)$$ n/a 3776 8
8007.2.cm $$\chi_{8007}(179, \cdot)$$ n/a 7552 8
8007.2.cp $$\chi_{8007}(16, \cdot)$$ n/a 5712 12
8007.2.cq $$\chi_{8007}(118, \cdot)$$ n/a 5664 12
8007.2.ct $$\chi_{8007}(1531, \cdot)$$ n/a 5040 12
8007.2.cu $$\chi_{8007}(52, \cdot)$$ n/a 10128 24
8007.2.cv $$\chi_{8007}(292, \cdot)$$ n/a 7584 16
8007.2.cy $$\chi_{8007}(22, \cdot)$$ n/a 7584 16
8007.2.da $$\chi_{8007}(326, \cdot)$$ n/a 15104 16
8007.2.db $$\chi_{8007}(641, \cdot)$$ n/a 15104 16
8007.2.dd $$\chi_{8007}(4, \cdot)$$ n/a 11328 24
8007.2.dg $$\chi_{8007}(98, \cdot)$$ n/a 22656 24
8007.2.dh $$\chi_{8007}(1070, \cdot)$$ n/a 22656 24
8007.2.dk $$\chi_{8007}(392, \cdot)$$ n/a 20256 24
8007.2.dl $$\chi_{8007}(149, \cdot)$$ n/a 22656 24
8007.2.dn $$\chi_{8007}(310, \cdot)$$ n/a 11424 24
8007.2.dq $$\chi_{8007}(577, \cdot)$$ n/a 11424 24
8007.2.dt $$\chi_{8007}(205, \cdot)$$ n/a 10128 24
8007.2.du $$\chi_{8007}(424, \cdot)$$ n/a 11328 24
8007.2.dx $$\chi_{8007}(59, \cdot)$$ n/a 45312 48
8007.2.dy $$\chi_{8007}(49, \cdot)$$ n/a 22848 48
8007.2.dz $$\chi_{8007}(196, \cdot)$$ n/a 22656 48
8007.2.ed $$\chi_{8007}(2, \cdot)$$ n/a 45312 48
8007.2.ef $$\chi_{8007}(208, \cdot)$$ n/a 22656 48
8007.2.eg $$\chi_{8007}(200, \cdot)$$ n/a 45312 48
8007.2.ei $$\chi_{8007}(137, \cdot)$$ n/a 40416 48
8007.2.el $$\chi_{8007}(152, \cdot)$$ n/a 45312 48
8007.2.en $$\chi_{8007}(38, \cdot)$$ n/a 45312 48
8007.2.ep $$\chi_{8007}(106, \cdot)$$ n/a 22848 48
8007.2.eq $$\chi_{8007}(316, \cdot)$$ n/a 45504 96
8007.2.et $$\chi_{8007}(7, \cdot)$$ n/a 45504 96
8007.2.ev $$\chi_{8007}(56, \cdot)$$ n/a 90624 96
8007.2.ew $$\chi_{8007}(14, \cdot)$$ n/a 90624 96
8007.2.ey $$\chi_{8007}(53, \cdot)$$ n/a 90624 96
8007.2.fc $$\chi_{8007}(19, \cdot)$$ n/a 45312 96
8007.2.fd $$\chi_{8007}(25, \cdot)$$ n/a 45696 96
8007.2.fe $$\chi_{8007}(26, \cdot)$$ n/a 90624 96
8007.2.fh $$\chi_{8007}(11, \cdot)$$ n/a 181248 192
8007.2.fi $$\chi_{8007}(44, \cdot)$$ n/a 181248 192
8007.2.fk $$\chi_{8007}(73, \cdot)$$ n/a 91008 192
8007.2.fn $$\chi_{8007}(61, \cdot)$$ n/a 91008 192

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

## Decomposition of $$S_{2}^{\mathrm{old}}(\Gamma_1(8007))$$ into lower level spaces

$$S_{2}^{\mathrm{old}}(\Gamma_1(8007)) \cong$$ $$S_{2}^{\mathrm{new}}(\Gamma_1(17))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(51))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(157))$$$$^{\oplus 4}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(471))$$$$^{\oplus 2}$$$$\oplus$$$$S_{2}^{\mathrm{new}}(\Gamma_1(2669))$$$$^{\oplus 2}$$

## Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ ($$1 - T + 2 T^{2}$$)($$1 + 2 T + 3 T^{2} + 4 T^{3} + 4 T^{4}$$)
$3$ ($$1 + T$$)($$( 1 - T )^{2}$$)
$5$ ($$1 + 5 T^{2}$$)($$1 + 4 T + 12 T^{2} + 20 T^{3} + 25 T^{4}$$)
$7$ ($$1 - 2 T + 7 T^{2}$$)($$1 + 4 T + 16 T^{2} + 28 T^{3} + 49 T^{4}$$)
$11$ ($$1 - 4 T + 11 T^{2}$$)($$1 + 14 T^{2} + 121 T^{4}$$)
$13$ ($$1 - 2 T + 13 T^{2}$$)($$1 - 6 T^{2} + 169 T^{4}$$)
$17$ ($$1 - T$$)($$( 1 + T )^{2}$$)
$19$ ($$1 + 4 T + 19 T^{2}$$)($$1 + 4 T + 34 T^{2} + 76 T^{3} + 361 T^{4}$$)
$23$ ($$1 + 6 T + 23 T^{2}$$)($$1 - 8 T + 60 T^{2} - 184 T^{3} + 529 T^{4}$$)
$29$ ($$1 + 4 T + 29 T^{2}$$)($$1 - 4 T + 12 T^{2} - 116 T^{3} + 841 T^{4}$$)
$31$ ($$1 + 31 T^{2}$$)($$1 - 8 T + 70 T^{2} - 248 T^{3} + 961 T^{4}$$)
$37$ ($$1 + 2 T + 37 T^{2}$$)($$1 - 4 T + 70 T^{2} - 148 T^{3} + 1369 T^{4}$$)
$41$ ($$1 + 41 T^{2}$$)($$1 - 4 T + 84 T^{2} - 164 T^{3} + 1681 T^{4}$$)
$43$ ($$1 - 4 T + 43 T^{2}$$)($$1 - 42 T^{2} + 1849 T^{4}$$)
$47$ ($$1 + 47 T^{2}$$)($$1 - 12 T + 98 T^{2} - 564 T^{3} + 2209 T^{4}$$)
$53$ ($$1 + 2 T + 53 T^{2}$$)($$( 1 + 4 T + 53 T^{2} )^{2}$$)
$59$ ($$1 - 4 T + 59 T^{2}$$)($$( 1 + 6 T + 59 T^{2} )^{2}$$)
$61$ ($$1 - 12 T + 61 T^{2}$$)($$1 - 8 T + 136 T^{2} - 488 T^{3} + 3721 T^{4}$$)
$67$ ($$1 + 4 T + 67 T^{2}$$)($$1 - 8 T + 22 T^{2} - 536 T^{3} + 4489 T^{4}$$)
$71$ ($$1 - 8 T + 71 T^{2}$$)($$( 1 + 8 T + 71 T^{2} )^{2}$$)
$73$ ($$1 + 4 T + 73 T^{2}$$)($$1 + 16 T + 208 T^{2} + 1168 T^{3} + 5329 T^{4}$$)
$79$ ($$1 + 10 T + 79 T^{2}$$)($$1 - 12 T + 96 T^{2} - 948 T^{3} + 6241 T^{4}$$)
$83$ ($$1 + 16 T + 83 T^{2}$$)($$1 + 4 T + 162 T^{2} + 332 T^{3} + 6889 T^{4}$$)
$89$ ($$1 + 6 T + 89 T^{2}$$)($$1 - 12 T + 86 T^{2} - 1068 T^{3} + 7921 T^{4}$$)
$97$ ($$1 + 12 T + 97 T^{2}$$)($$1 + 176 T^{2} + 9409 T^{4}$$)