Properties

Label 8002.2
Level 8002
Weight 2
Dimension 666999
Nonzero newspaces 20
Sturm bound 8004000

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Defining parameters

Level: \( N \) = \( 8002 = 2 \cdot 4001 \)
Weight: \( k \) = \( 2 \)
Nonzero newspaces: \( 20 \)
Sturm bound: \(8004000\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(8002))\).

Total New Old
Modular forms 2005000 666999 1338001
Cusp forms 1997001 666999 1330002
Eisenstein series 7999 0 7999

Decomposition of \(S_{2}^{\mathrm{new}}(\Gamma_1(8002))\)

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
8002.2.a \(\chi_{8002}(1, \cdot)\) 8002.2.a.a 1 1
8002.2.a.b 1
8002.2.a.c 1
8002.2.a.d 69
8002.2.a.e 77
8002.2.a.f 89
8002.2.a.g 95
8002.2.b \(\chi_{8002}(8001, \cdot)\) n/a 334 1
8002.2.c \(\chi_{8002}(899, \cdot)\) n/a 668 2
8002.2.d \(\chi_{8002}(1401, \cdot)\) n/a 1336 4
8002.2.e \(\chi_{8002}(2915, \cdot)\) n/a 1336 4
8002.2.f \(\chi_{8002}(3099, \cdot)\) n/a 1336 4
8002.2.g \(\chi_{8002}(1115, \cdot)\) n/a 2664 8
8002.2.h \(\chi_{8002}(1305, \cdot)\) n/a 2672 8
8002.2.i \(\chi_{8002}(201, \cdot)\) n/a 6680 20
8002.2.k \(\chi_{8002}(673, \cdot)\) n/a 5344 16
8002.2.l \(\chi_{8002}(625, \cdot)\) n/a 6680 20
8002.2.m \(\chi_{8002}(121, \cdot)\) n/a 10656 32
8002.2.n \(\chi_{8002}(25, \cdot)\) n/a 13360 40
8002.2.o \(\chi_{8002}(35, \cdot)\) n/a 33400 100
8002.2.q \(\chi_{8002}(5, \cdot)\) n/a 26720 80
8002.2.r \(\chi_{8002}(65, \cdot)\) n/a 33400 100
8002.2.s \(\chi_{8002}(59, \cdot)\) n/a 53280 160
8002.2.t \(\chi_{8002}(49, \cdot)\) n/a 66800 200
8002.2.v \(\chi_{8002}(7, \cdot)\) n/a 133600 400
8002.2.w \(\chi_{8002}(9, \cdot)\) n/a 266400 800

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

Decomposition of \(S_{2}^{\mathrm{old}}(\Gamma_1(8002))\) into lower level spaces

\( S_{2}^{\mathrm{old}}(\Gamma_1(8002)) \cong \) \(S_{2}^{\mathrm{new}}(\Gamma_1(4001))\)\(^{\oplus 2}\)

Hecke Characteristic Polynomials

$p$ $F_p(T)$
$2$ (\( 1 - T \))(\( 1 - T \))(\( 1 - T \))
$3$ (\( 1 + T + 3 T^{2} \))(\( 1 + 3 T^{2} \))(\( 1 - 2 T + 3 T^{2} \))
$5$ (\( 1 - T + 5 T^{2} \))(\( 1 + 5 T^{2} \))(\( 1 + 2 T + 5 T^{2} \))
$7$ (\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))(\( 1 + 7 T^{2} \))
$11$ (\( 1 + 11 T^{2} \))(\( 1 + 2 T + 11 T^{2} \))(\( 1 + 6 T + 11 T^{2} \))
$13$ (\( 1 - 2 T + 13 T^{2} \))(\( 1 - 4 T + 13 T^{2} \))(\( 1 - 2 T + 13 T^{2} \))
$17$ (\( 1 - 4 T + 17 T^{2} \))(\( 1 + 17 T^{2} \))(\( 1 + 2 T + 17 T^{2} \))
$19$ (\( 1 + 4 T + 19 T^{2} \))(\( 1 - T + 19 T^{2} \))(\( 1 - 8 T + 19 T^{2} \))
$23$ (\( 1 - T + 23 T^{2} \))(\( 1 - 3 T + 23 T^{2} \))(\( 1 - 4 T + 23 T^{2} \))
$29$ (\( 1 + 6 T + 29 T^{2} \))(\( 1 + 4 T + 29 T^{2} \))(\( 1 + 6 T + 29 T^{2} \))
$31$ (\( 1 + 6 T + 31 T^{2} \))(\( 1 + 31 T^{2} \))(\( 1 + 31 T^{2} \))
$37$ (\( 1 + 6 T + 37 T^{2} \))(\( 1 - 6 T + 37 T^{2} \))(\( 1 + 37 T^{2} \))
$41$ (\( 1 - 10 T + 41 T^{2} \))(\( 1 + 8 T + 41 T^{2} \))(\( 1 + 2 T + 41 T^{2} \))
$43$ (\( 1 + 9 T + 43 T^{2} \))(\( 1 + 12 T + 43 T^{2} \))(\( 1 + 6 T + 43 T^{2} \))
$47$ (\( 1 - 6 T + 47 T^{2} \))(\( 1 + 10 T + 47 T^{2} \))(\( 1 + 47 T^{2} \))
$53$ (\( 1 + 4 T + 53 T^{2} \))(\( 1 + 13 T + 53 T^{2} \))(\( 1 + 4 T + 53 T^{2} \))
$59$ (\( 1 + 59 T^{2} \))(\( 1 - 7 T + 59 T^{2} \))(\( 1 + 59 T^{2} \))
$61$ (\( 1 + 9 T + 61 T^{2} \))(\( 1 - 12 T + 61 T^{2} \))(\( 1 + 6 T + 61 T^{2} \))
$67$ (\( 1 + T + 67 T^{2} \))(\( 1 + 16 T + 67 T^{2} \))(\( 1 - 2 T + 67 T^{2} \))
$71$ (\( 1 + 2 T + 71 T^{2} \))(\( 1 - 8 T + 71 T^{2} \))(\( 1 + 8 T + 71 T^{2} \))
$73$ (\( 1 - 4 T + 73 T^{2} \))(\( 1 - 4 T + 73 T^{2} \))(\( 1 - 10 T + 73 T^{2} \))
$79$ (\( 1 + 10 T + 79 T^{2} \))(\( 1 - 10 T + 79 T^{2} \))(\( 1 + 16 T + 79 T^{2} \))
$83$ (\( 1 - 12 T + 83 T^{2} \))(\( 1 + 4 T + 83 T^{2} \))(\( 1 + 12 T + 83 T^{2} \))
$89$ (\( 1 - 7 T + 89 T^{2} \))(\( 1 - 15 T + 89 T^{2} \))(\( 1 + 2 T + 89 T^{2} \))
$97$ (\( 1 + T + 97 T^{2} \))(\( 1 - 10 T + 97 T^{2} \))(\( 1 - 2 T + 97 T^{2} \))
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