Properties

Label 6008.2
Level 6008
Weight 2
Dimension 633000
Nonzero newspaces 24
Sturm bound 4512000

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Defining parameters

Level: \( N \) = \( 6008 = 2^{3} \cdot 751 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 24 \)
Sturm bound: \(4512000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(6008))\).

Total New Old
Modular forms 1132500 635996 496504
Cusp forms 1123501 633000 490501
Eisenstein series 8999 2996 6003

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(6008))\)

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
6008.2.a \(\chi_{6008}(1, \cdot)\) 6008.2.a.a 1 1
6008.2.a.b 44
6008.2.a.c 44
6008.2.a.d 49
6008.2.a.e 50
6008.2.b \(\chi_{6008}(3003, \cdot)\) n/a 750 1
6008.2.c \(\chi_{6008}(3005, \cdot)\) n/a 750 1
6008.2.h \(\chi_{6008}(6007, \cdot)\) None 0 1
6008.2.i \(\chi_{6008}(4433, \cdot)\) n/a 376 2
6008.2.j \(\chi_{6008}(569, \cdot)\) n/a 752 4
6008.2.k \(\chi_{6008}(679, \cdot)\) None 0 2
6008.2.p \(\chi_{6008}(1429, \cdot)\) n/a 1500 2
6008.2.q \(\chi_{6008}(3683, \cdot)\) n/a 1500 2
6008.2.r \(\chi_{6008}(359, \cdot)\) None 0 4
6008.2.w \(\chi_{6008}(2333, \cdot)\) n/a 3000 4
6008.2.x \(\chi_{6008}(291, \cdot)\) n/a 3000 4
6008.2.y \(\chi_{6008}(673, \cdot)\) n/a 1504 8
6008.2.z \(\chi_{6008}(193, \cdot)\) n/a 3760 20
6008.2.ba \(\chi_{6008}(675, \cdot)\) n/a 6000 8
6008.2.bb \(\chi_{6008}(437, \cdot)\) n/a 6000 8
6008.2.bg \(\chi_{6008}(583, \cdot)\) None 0 8
6008.2.bi \(\chi_{6008}(799, \cdot)\) None 0 20
6008.2.bl \(\chi_{6008}(53, \cdot)\) n/a 15000 20
6008.2.bn \(\chi_{6008}(195, \cdot)\) n/a 15000 20
6008.2.bo \(\chi_{6008}(121, \cdot)\) n/a 7520 40
6008.2.bp \(\chi_{6008}(49, \cdot)\) n/a 18800 100
6008.2.br \(\chi_{6008}(61, \cdot)\) n/a 30000 40
6008.2.bt \(\chi_{6008}(11, \cdot)\) n/a 30000 40
6008.2.bv \(\chi_{6008}(223, \cdot)\) None 0 40
6008.2.bz \(\chi_{6008}(7, \cdot)\) None 0 100
6008.2.ca \(\chi_{6008}(27, \cdot)\) n/a 75000 100
6008.2.cb \(\chi_{6008}(45, \cdot)\) n/a 75000 100
6008.2.ce \(\chi_{6008}(9, \cdot)\) n/a 37600 200
6008.2.ch \(\chi_{6008}(5, \cdot)\) n/a 150000 200
6008.2.ci \(\chi_{6008}(15, \cdot)\) None 0 200
6008.2.cj \(\chi_{6008}(3, \cdot)\) n/a 150000 200

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(6008))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(6008)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(751))\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(1502))\)\(^{\oplus 3}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(\Gamma_1(3004))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ 1
$3$ (\( 1 + 3 T^{2} \))
$5$ (\( 1 + 2 T + 5 T^{2} \))
$7$ (\( 1 + 4 T + 7 T^{2} \))
$11$ (\( 1 + 11 T^{2} \))
$13$ (\( 1 + T + 13 T^{2} \))
$17$ (\( 1 + 6 T + 17 T^{2} \))
$19$ (\( 1 - 3 T + 19 T^{2} \))
$23$ (\( 1 + 9 T + 23 T^{2} \))
$29$ (\( 1 + 10 T + 29 T^{2} \))
$31$ (\( 1 + 8 T + 31 T^{2} \))
$37$ (\( 1 - 11 T + 37 T^{2} \))
$41$ (\( 1 + 41 T^{2} \))
$43$ (\( 1 + 4 T + 43 T^{2} \))
$47$ (\( 1 + 3 T + 47 T^{2} \))
$53$ (\( 1 + T + 53 T^{2} \))
$59$ (\( 1 + 13 T + 59 T^{2} \))
$61$ (\( 1 - 3 T + 61 T^{2} \))
$67$ (\( 1 - 8 T + 67 T^{2} \))
$71$ (\( 1 + 8 T + 71 T^{2} \))
$73$ (\( 1 + 4 T + 73 T^{2} \))
$79$ (\( 1 - 6 T + 79 T^{2} \))
$83$ (\( 1 - 6 T + 83 T^{2} \))
$89$ (\( 1 + 5 T + 89 T^{2} \))
$97$ (\( 1 + 3 T + 97 T^{2} \))
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