Properties

Label 8007.2
Level 8007
Weight 2
Dimension 1757543
Nonzero newspaces 72
Sturm bound 9464832

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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

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